\ifdefined\target\else
  \def\target{draft}
\fi

\documentclass[\target,fleqn,reqno,11pt]{article}
\usepackage[table, subgroups]{svn-multi}
\svnid{$Id: reps.tex 433 2015-05-19 22:16:57Z mariano $}
\usepackage[utf8]{inputenc}
\usepackage[main=english,german,french,shorthands=off]{babel}
\usepackage{etex}
\usepackage{ifdraft}
\usepackage{excludeonly}
\usepackage{xifthen}
\usepackage{multicol}
\usepackage{lipsum}
\usepackage[a4paper]{geometry}
\usepackage[hyphens]{url}
\usepackage[osf,noBBpl]{mathpazo}
\usepackage[T1]{fontenc}
\usepackage{mathrsfs}
\usepackage[final]{microtype}
\usepackage[nobottomtitles*]{titlesec}
\usepackage{paragraphs}
\usepackage{enumitem}
\usepackage{array}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{textcomp}
\usepackage{stmaryrd}
\usepackage{colonequals}
\usepackage{mathtools}
\usepackage[matrix,arrow]{xypic}
\usepackage{xcolor}
\usepackage{booktabs}
\usepackage{varioref}
\usepackage{helvet}
\usepackage{comment}
\usepackage{everypage}
\usepackage{fancyhdr}
\usepackage{tikz}
\usetikzlibrary{
        cd,
        matrix,
        decorations.pathreplacing, 
        calc, 
        positioning,
        arrows.meta,
        external
        }
%\tikzexternalize

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}

% slightly larger leading, for regularity
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% let \[ and \] be the same as \begin{equation} and \end{equation}
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}
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% but only print equation numbers if needed
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\usepackage{hyperref}
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  final, 
  colorlinks, 
  linkcolor=-red!75!green!50, 
  citecolor=cite-color,
  urlcolor=green!30!black
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% sectioning

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  \titlerule
  \vspace{1pc}%
  \LARGE\MakeUppercase{Chapter} \thesection}
  {1pc}
  {\titlerule
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  \Huge}[\vspace{3pc}]
%\titleformat{\section}
%  {\filcenter\color{pretty-title}\normalfont\Huge\bfseries\sffamily}
%  {\thesection.\space}{0em}{\vspace{1cm}}
\titleformat{\subsection}
  {\normalfont\color{pretty-title}\sffamily\bfseries\large\filcenter}
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  {0pt}{8ex plus 1ex minus .5ex}{1.5ex plus .2ex}

\newcommand\sectionbreak{\clearpage}

\setcounter{tocdepth}{2}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% amsrefs has to come after hyperref for back references in the
% bibliography to work. Also, xypic defines \cir, and amsrefs indirectly
% does the same, so...

\let\cir\relax 
\usepackage[alphabetic, nobysame, y2k, msc-links]{amsrefs}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% theorems and such
\usepackage{amsthm}
\usepackage{thmtools}
\declaretheoremstyle[
        headformat=\NUMBER.\hskip.75ex\NAME\NOTE,
        spaceabove=\paraskip, 
        headfont=\bfseries,
        bodyfont=\itshape
        ]{mystyle}
\declaretheoremstyle[
        numbered=no, 
        spaceabove=\paraskip, 
        bodyfont=\itshape,
        ]{mystyleempty}
\declaretheoremstyle[
        headformat={{\bfseries\NUMBER.\hskip0.25ex}},
        spaceabove=\paraskip, 
        headpunct={},
        bodyfont=\normalfont
        ]{mystyleplain}
\declaretheorem[sibling=para, style=mystyle]{Lemma}
\declaretheorem[style=mystyleempty, name=Lemma]{Lemma*}
\declaretheorem[sibling=para, style=mystyle]{Proposition}
\declaretheorem[style=mystyleempty, name=Proposition]{Proposition*}
\declaretheorem[sibling=para, style=mystyle]{Theorem}
\declaretheorem[style=mystyleempty, name=Theorem]{Theorem*}
\declaretheorem[sibling=para, style=mystyle]{Corollary}
\declaretheorem[style=mystyleempty, name=Corollary]{Corollary*}
\declaretheorem[sibling=para, style=mystyleplain]{Exercise}

% this comes from http://tex.stackexchange.com/a/17465/525
% at some point this should be replaced by the automatic variant 
% described there...
\makeatletter
\newlength{\@thlabel@width}
\newcommand{\fixhspace}{%
        \settowidth{\@thlabel@width}{\itshape1.}%
        \sbox{\@labels}{%
                \unhbox\@labels%
                \hspace{\dimexpr-\leftmargin+\labelsep+\@thlabel@width-\itemindent}
                }
        }
\makeatother

\newenvironment{Hint}{\textit{Hint.}}{}

% list inside theorems
\newlist{thmlist}{enumerate}{1}
\setlist[thmlist]{
        nolistsep,
        ref={\mdseries\textup{(\emph{\roman*})}},
        label={\mdseries\textup{(\emph{\roman*})}},
        %before={\advance\mathindent\leftmargin}
        }
\newcommand\thmitem[1]{\textup{(\emph{\romannumeral #1})}}

% TFAEs
\newlist{tfae}{enumerate}{1}
\setlist[tfae]{
        nolistsep,
        ref={\mdseries\textup{(\emph{\alph*})}},
        label={\mdseries\textup{(\emph{\alph*})}},
        before={\advance\mathindent\leftmargin}}
\makeatletter
\newcommand\tfaeitem[1]{{\textup{(\emph{\@alph #1})}}}
\newcommand\implication[2]{$\mbox{\tfaeitem{#1}}\Rightarrow\mbox{\tfaeitem{#2}}$}
\makeatother

% textual claims in equations
\newcommand\claim[2][.8]{%
  \begin{minipage}{#1\displaywidth}%
  \itshape
  #2
  \end{minipage}%
}

% we redefine amsthm's proof so that the \topsep is equal to our \paraskip
\makeatletter
\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \topsep0pt%
  \trivlist
  \item[\hskip\labelsep
        \itshape
    #1\@addpunct{.}]\ignorespaces
}{%
  \popQED\endtrivlist\@endpefalse
}
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% caption wans to be after thmtools...
\usepackage{caption}
\captionsetup{
  font=small, 
  labelfont=bf,
  margin=30pt,
  labelsep=period,
}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% this should be last

\ifdraft{
  \usepackage[draft]{showlabels}
  \renewcommand\showlabelfont{\small\sffamily\color{green!70!black}}
}{}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% the TOC

\makeatletter
\renewcommand\tableofcontents{%
  \footnotesize
  \@starttoc{toc}
}
\makeatother

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% a sans serif font for operator names

% from http://tex.stackexchange.com/questions/43131/the-font-of-operator-names
% and http://tex.stackexchange.com/questions/60891/the-font-of-operator-names-the-size
\DeclareFontFamily{OT1}{slmss}{}
\DeclareFontShape{OT1}{slmss}{m}{n}
     {<-8.5> s*[1.1] rm-lmss8
      <8.5-9.5> s*[1.1] rm-lmss9
      <9.5-11> s*[1.1] rm-lmss10
      <11-15.5> s*[1.1] rm-lmss12
      <15.5-> s*[1.1] rm-lmss17
     }{}
\DeclareSymbolFont{sfoperators}{OT1}{slmss}{m}{n}
\DeclareSymbolFontAlphabet{\mathsf}{sfoperators}
\makeatletter
\def\operator@font{\mathgroup\symsfoperators}
\makeatother

% declare a font family for the mathabx a font
\DeclareFontFamily{U}{mathb}{\hyphenchar\font45}
\DeclareFontShape{U}{mathb}{m}{n}{
  <-6> mathb5 <6-7> mathb6 <7-8> mathb7
  <8-9> mathb8 <9-10> mathb9
  <10-12> mathb10 <12-> mathb12
  }{}

% from http://tex.stackexchange.com/a/14406/525
\usepackage{pifont}
\makeatletter
\newcommand\Pimathsymbol[3][\mathord]{%
  #1{\@Pimathsymbol{#2}{#3}}}
\def\@Pimathsymbol#1#2{\mathchoice
  {\@Pim@thsymbol{#1}{#2}\tf@size}
  {\@Pim@thsymbol{#1}{#2}\tf@size}
  {\@Pim@thsymbol{#1}{#2}\sf@size}
  {\@Pim@thsymbol{#1}{#2}\ssf@size}}
\def\@Pim@thsymbol#1#2#3{%
  \mbox{\fontsize{#3}{#3}\Pisymbol{#1}{#2}}}
\makeatother


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% locally useful commands

\newcommand\NN{\mathbb{N}}
\newcommand\ZZ{\mathbb{Z}}
\newcommand\QQ{\mathbb{Q}}
\newcommand\CC{\mathbb{C}}
\let\eps\varepsilon
\newcommand\A{\mathscr{A}}
\newcommand\B{\mathscr{B}}
\newcommand\J{\mathscr{J}}
\newcommand\Jac[1]{{J(#1)}}
\renewcommand\L{\mathscr{L}}
\newcommand\N{\mathscr{N}}
\let\oldS\S
\let\S\relax
\renewcommand\O{\mathcal{O}}
\newcommand\S{\mathscr{S}}
\newcommand\E{\mathscr{E}}
\newcommand\C{\mathscr{C}}
\newcommand\id{\mathrm{id}}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
\DeclarePairedDelimiter\lin{\langle}{\rangle}
\DeclarePairedDelimiter\pd{\lparen}{\rparen}
\DeclareMathOperator{\Z}{Z} % center
\DeclareMathOperator{\tr}{tr} % trace
\DeclareMathOperator{\coker}{coker} 
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\Ext}{Ext}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\soc}{soc}
\DeclareMathOperator{\rad}{rad}
\let\r\relax
\DeclareMathOperator{\r}{r}
\DeclareMathOperator{\ann}{ann}
\DeclareMathOperator{\Frac}{Frac}
\let\top\relax
\DeclarePairedDelimiter\cls{\lbrack}{\rbrack}
\DeclarePairedDelimiter\kls{\llbracket}{\rrbracket}
\DeclareMathOperator{\obj}{obj}
\DeclareMathOperator{\top}{top}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\cl}{cl}
\DeclareMathOperator{\Disc}{Disc}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\ev}{ev}
\DeclareMathOperator{\sgn}{sgn}
\let\epsilon\varepsilon
\let\nbd\nobreakdash
\newcommand\kk{\Bbbk}
\newcommand\place{\mathord-}
\newcommand\todo[1][]{\textcolor{red}{\ifthenelse{\isempty{#1}}{To be done}{#1}}}
\newcommand\admono{\rightarrowtail}
\newcommand\adepi{\twoheadrightarrow}

\newcommand\dynkin[2]{\mathsf{#1}_{#2}}
\renewcommand\H{\mathscr{H}}

\newcommand\Alg{\mathsf{Alg}}
\newcommand\Grp{\mathsf{Grp}}
\newcommand\op{\mathsf{op}}
\newcommand\transp{\mathsf{t}}
\newcommand\lRep[1]{{}_{#1}\mathsf{Rep}}
\newcommand\lrep[1]{{}_{#1}\mathsf{rep}}
\newcommand\lMod[1]{{}_{#1}\mathsf{Mod}}
\newcommand\rMod[1]{\mathsf{Mod}_{#1}}
\newcommand\lmod[1]{{}_{#1}\mathsf{mod}}
\newcommand\rmod[1]{\mathsf{mod}_{#1}}
\newcommand\lpmod[1]{{}_{#1}\underline{\mathsf{mod}}}
\newcommand\rpmod[1]{\underline{\mathsf{mod}}_{#1}}
\newcommand\lproy[1]{{}_{#1}\mathsf{proy}}
\newcommand\rproy[1]{\mathsf{proy}_{#1}}
\newcommand\ind[1]{{}_{#1}\mathsf{ind}}
\newcommand\simp[1]{{}_{#1}\mathsf{simp}}
\newcommand\markPO{\ar@{}[dr]|-{\mathsf{PO}}}
\newcommand\markPB{\ar@{}[dr]|-{\mathsf{PB}}}
\DeclareMathOperator\phom{\underline{hom}}
\DeclareMathOperator\Tr{Tr}

% we import these from mathabx; we only miss \precneq, but import the 
% whole set so that they look the same
\renewcommand\prec{\Pimathsymbol[\mathrel]{mathb}{"A0}}
\renewcommand\nprec{\Pimathsymbol[\mathrel]{mathb}{"A2}}
\renewcommand\preceq{\Pimathsymbol[\mathrel]{mathb}{"A8}}
\newcommand\precneq{\Pimathsymbol[\mathrel]{mathb}{"AC}}
\newcommand\covered{\Pimathsymbol[\mathrel]{mathb}{"CC}}

% defs

\newcommand\newterm[1]{%
  \textcolor{newterm-color}{\bfseries\itshape #1}%
}

\newcommand\afterstatement{\par\smallskip\noindent\ignorespaces}

% this comes froma http://tex.stackexchange.com/a/23110/525
\makeatletter
\def\ignorespacesandallpars{%
  \begingroup
  \catcode13=10
  \@ifnextchar\par
    {\endgroup\expandafter\ignorespacesandallpars\@gobble}%
    {\endgroup}%
}
\makeatother

\ifdraft{%
  \newcommand\note[1]{%
    \marginpar{%
      \footnotesize\sffamily\color{red}\raggedright
      \rule[1pt]{5pt}{5pt}\ #1
    }%
  }%
}{%
  \newcommand\note[1]{}%
}

\ifdraft{
  \let\framed\relax
  \usepackage{framed}
  \definecolor{shadecolor}{gray}{0.85}
  \newenvironment{Solution}[1][Soluci\'on]{
    \begingroup
    \begin{shaded}
    \noindent\small\textit{#1. }%
    \ignorespacesandallpars}%
   {\end{shaded}
   \endgroup
   }
}{
  \specialcomment{Solution}{}{}
  \excludecomment{Solution}
}

\newenvironment{alert}
   {\hfill\begin{minipage}{.6\textwidth}\flushright\small\sffamily}
   {\end{minipage}\bigskip\penalty10000}

\setitemize{nolistsep, listparindent=\parindent}

\hyphenation{
  indeed Indeed actually implies linear order basis
  hypo-thesis sub-complex complex image Appendix semi-simple
  action
}

\makeindex

\ifdraft{
\includeonly{ar}
}{}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{Representations}

\author{Mariano Suárez-Álvarez}

\date{\today}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setcounter{page}{0}

\maketitle

\thispagestyle{firstpage}

\begingroup
  \columnsep=1cm%
  \begin{multicols*}{2}
    \tableofcontents
  \end{multicols*}
\endgroup

\ifdraft{
  \setcounter{page}{0}\thispagestyle{empty}\tableofrevisions
}{}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\include{reduction}
\include{semisimple}
\include{groups}
\include{radical}
\include{projectives}
\include{ar}
\appendix
\include{homological}
\include{references}

\end{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%vim: tw=70 fileencoding=latin1
