notes.sty

\usepackage[utf8x]{inputenc} % try to encode as UTF-8 extended.  Remove the 'x' for regular UTF-8.  See https://en.wikibooks.org/wiki/LaTeX/Special_Characters#A_technical_matter
\usepackage{amssymb,mathrsfs,amsmath}
\usepackage{mathtools}
\usepackage{tikz}
\usepackage{upgreek}
\usepackage{color}
%% Some user-defined colors
	\definecolor{mydefi}{cmyk}{1,0,0,.5}
	\definecolor{myred}{rgb}{.7,.1,.1}
	\definecolor{myblue}{rgb}{.1,.1,.6}
	\definecolor{mygreen}{rgb}{.1,.6,.1}
\usepackage[urlbordercolor={1 1 1}, pdfborder={0 0 0}, bookmarks=true,
  colorlinks=true, linkcolor=myblue, citecolor=myblue,
  urlcolor=myblue, hyperfootnotes=false]{hyperref}
\usepackage[alphabetic,abbrev]{amsrefs} % use AMS ref scheme
\usepackage{enumitem}



\addtolength{\footskip}{2\baselineskip} % to lower the page numbers


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  MACRO DEFINITIONS:  Co-authors -- PLEASE use these!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\defeq}{\coloneqq} % defined to be equal to (the := symbol)
\newcommand{\eqdef}{\eqqcolon} % equal by definition (the =: symbol)
\newcommand{\interior}[1]{\overset{\circ}{#1}}
\newcommand{\coker}{\operatorname{coker}}% cokernel
\newcommand{\Tor}{\operatorname{Tor}} % Torsion
\newcommand{\boundary}{\partial} % for the "boundary" of a topological space/manifold/etc
\newcommand{\bdy}{\boundary} % shorthand for "boundary"
\renewcommand{\d}{\,\operatorname{d}} % for the "d" at the end of an integral % you can delete this if you don't like it.  it's debatable.
\newcommand{\tprod}{\otimes} % tensor product
\newcommand{\dsum}{\oplus} % direct sum
\newcommand{\Dsum}{\Oplus} % `big' direct sum
\newcommand{\dunion}{\sqcup} % disjoint union
\newcommand{\Dunion}{\bigsqcup} % `big' disjoint union
\newcommand{\union}{\cup} % union
\newcommand{\Union}{\bigcup} % `big' union
\newcommand{\intersect}{\cap} % intersection
\newcommand{\Intersect}{\bigcap} % `big' intersection
\newcommand{\suchthat}{\mid} % for the "such that" symbol in a set definition
\newcommand{\st}{\suchthat} % shorthand for "such that"
\newcommand{\from}{\colon} % for use in $f \from X \to Y$
\newcommand{\into}{\hookrightarrow} % for use in $f \from X \into Y$ (injective)
\newcommand{\onto}{\twoheadrightarrow} % for use in $f \from X \onto Y$ (surjective)
\newcommand{\isomto}{\overset{\sim}{\to}} % for use in $f \from X \isomto Y$ (isomorphism)
\newcommand{\bij}{\longleftrightarrow} % for use in $f \from X \bij Y$ (bijective)
\newcommand{\lto}{\leftarrow}
\newcommand{\linto}{\hookleftarrow} % for use in $f \from X \into Y$ (injective)
\newcommand{\lonto}{\twoheadleftarrow} % for use in $f \from X \onto Y$ (surjective)
\newcommand{\lisomto}{\overset{\sim}{\lto}} % for use in $f \from X \isomto Y$ (isomorphism)
\newcommand{\actson}{\curvearrowright}
\newcommand{\limplies}{\Longleftarrow} % left implies.  Implies, but in the opposite direction.
\newcommand{\im}{\operatorname{Im}} % for "Image" of a function
\newcommand{\rank}{\operatorname{rank}} % for "rank" of a function
\newcommand{\of}{\circ} % function composition
\newcommand{\de}{\underline} % for newly defined terms
\newcommand{\Ob}{\operatorname{Ob}} % Object family in a category
\newcommand{\morph}{\operatorname{morph}} % morphism family in a category
\newcommand{\oo}{\infty} % shorthand for "infinity"
\newcommand{\N}{{\mathbb N}} % natural numbers
\newcommand{\Z}{{\mathbb Z}} % integers
\newcommand{\Q}{{\mathbb Q}} % rational numbers
\newcommand{\R}{{\mathbb R}} % real numbers
\newcommand{\C}{{\mathbb C}} % complex numbers
\renewcommand{\H}{{\mathbb H}} % quaternions
\newcommand{\del}{\triangledown} % the Del operator
\newcommand{\vol}{\operatorname{Vol}} % volume
\newcommand{\Hom}{\operatorname{Hom}} % homomorphisms
\newcommand{\End}{\operatorname{End}} % endomorphisms
\newcommand{\Aut}{\operatorname{Aut}} % automorphisms
\newcommand{\free}[1]{\langle{#1}\rangle} % the free group generated by #1
\newcommand{\freeabelian}{\Z\free} % the free group generated by #1
\newcommand{\freeabel}{\freeabelian} % shorthand for the free abelian group generated by #1
\newcommand{\GL}{\operatorname{GL}} % general linear group
\newcommand{\B}{\mathfrak{B}} % use for the Borel sets.
\newcommand{\Sym}{\mathfrak{S}} % symmetic group
\newcommand{\sgn}{\operatorname{sgn}} % sign
\newcommand{\T}{\mathsf{T}} % use for tableaux
\newcommand{\U}{\mathsf{U}} % use for tableaux
\newcommand{\V}{\mathsf{V}} % use for tableaux
\newcommand{\TA}{\mathsf{A}} % use for tableaux
\newcommand{\TB}{\mathsf{B}} % use for tableaux
\newcommand{\TC}{\mathsf{C}} % use for tableaux
\newcommand{\TS}{\mathsf{S}} % use for tableaux
\newcommand{\shape}{\operatorname{shape}} % shape of a tableau
\newcommand{\col}[2]{\genfrac{}{}{0pt}{1}{#1}{#2}} % column of bitableau
\newcommand{\ov}{\overline} % shorthand for a bar on a symbol
\newcommand{\dd}{\partial} % use for diagram basis; e.g. d(V_l)
\newcommand{\X}{\mathcal{X}} % use for the Gelfand-Tsetlin subalgebra
\newcommand{\JM}{\mathcal{J}} % a subalgebra of the GT-subalgebra
\newcommand{\Std}{\operatorname{Std}} % set of standard tableaux
\newcommand{\StdB}{\operatorname{StdB}} % set of standard bitableaux
\newcommand{\Orb}{\mathcal{O}} % use for orbits
\newcommand{\OS}{\ov{\Orb}} % use for orbit sums
\newcommand{\OSS}{\ov{\OS}} % use for double bar orbit sums
\newcommand{\OR}{\mathscr{R}} % orbit representatives
\newcommand{\Stab}{\operatorname{Stab}} % stabilizer
\newcommand{\rev}{\operatorname{rev}} % reverse of a cycle
\newcommand{\A}{\mathcal{A}} % the algebra
\newcommand{\fraka}{\mathfrak{a}} % Young symmetrizer
\newcommand{\frakb}{\mathfrak{b}} % Young symmetrizer
\newcommand{\frakc}{\varphi} % canonical basis
\newcommand{\yy}{\mathsf{y}} % Young symmetrizer; scaled
\newcommand{\idem}{\varepsilon} % primitive central idem in symm gp
\newcommand{\cA}{\mathcal{A}} % group algebra of symmetric group
\newcommand{\Tab}{\operatorname{Tab}} % trails in branching graph from source
\newcommand{\BG}{\mathbf{B}} % branching graph
\newcommand{\bb}{\varnothing} % the unique element of \Irr(0)
\newcommand{\res}{\operatorname{res}} % restriction
\newcommand{\Irr}{\operatorname{Irr}} % irreps
\newcommand{\Wt}{\operatorname{Wt}} % possible content vectors for an irrep
\newcommand{\trace}{\operatorname{trace}} % the trace
\newcommand{\type}{\operatorname{type}} % type = generalized shape
\newcommand{\gen}[1]{\langle #1 \rangle} % use for generating sets
\newcommand{\parm}{\updelta} % Brauer algebra parameter
\newcommand{\sep}{\,|\,} % separator for two partitions - used in tables
\newcommand{\covered}{\lessdot}
\newcommand{\qand}{\quad\hbox{and}\quad}
\newcommand{\eqname}[1]{\tag*{#1}} % Tag equation with name
\newcommand{\propsubset}{\subsetneqq}
\newcommand{\sub}{\subset} % general 'contained in' symbol
\renewcommand{\Im}{\operatorname{Im}} % Imaginary part
\renewcommand{\Re}{\operatorname{Re}} % Real part
\newcommand{\norm}[1][\cdot]{\left\lVert#1\right\rVert} % norm command
\renewcommand{\d}{\, d} % For dx, d\mu, etc. in integrals to have some space.

%%%%%%%%%%%%%%%% BEGIN WIDEBAR COMMAND %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% this creates a \widebar command that has better width than both \bar and \overline %%%%%%
\makeatletter
\let\save@mathaccent\mathaccent
\newcommand*\if@single[3]{%
  \setbox0\hbox{${\mathaccent"0362{#1}}^H$}%
  \setbox2\hbox{${\mathaccent"0362{\kern0pt#1}}^H$}%
  \ifdim\ht0=\ht2 #3\else #2\fi
  }
%The bar will be moved to the right by a half of \macc@kerna, which is computed by amsmath:
\newcommand*\rel@kern[1]{\kern#1\dimexpr\macc@kerna}
%If there's a superscript following the bar, then no negative kern may follow the bar;
%an additional {} makes sure that the superscript is high enough in this case:
\newcommand*\widebar[1]{\@ifnextchar^{{\wide@bar{#1}{0}}}{\wide@bar{#1}{1}}}
%Use a separate algorithm for single symbols:
\newcommand*\wide@bar[2]{\if@single{#1}{\wide@bar@{#1}{#2}{1}}{\wide@bar@{#1}{#2}{2}}}
\newcommand*\wide@bar@[3]{%
  \begingroup
  \def\mathaccent##1##2{%
%Enable nesting of accents:
    \let\mathaccent\save@mathaccent
%If there's more than a single symbol, use the first character instead (see below):
    \if#32 \let\macc@nucleus\first@char \fi
%Determine the italic correction:
    \setbox\z@\hbox{$\macc@style{\macc@nucleus}_{}$}%
    \setbox\tw@\hbox{$\macc@style{\macc@nucleus}{}_{}$}%
    \dimen@\wd\tw@
    \advance\dimen@-\wd\z@
%Now \dimen@ is the italic correction of the symbol.
    \divide\dimen@ 3
    \@tempdima\wd\tw@
    \advance\@tempdima-\scriptspace
%Now \@tempdima is the width of the symbol.
    \divide\@tempdima 10
    \advance\dimen@-\@tempdima
%Now \dimen@ = (italic correction / 3) - (Breite / 10)
    \ifdim\dimen@>\z@ \dimen@0pt\fi
%The bar will be shortened in the case \dimen@<0 !
    \rel@kern{0.6}\kern-\dimen@
    \if#31
      \overline{\rel@kern{-0.6}\kern\dimen@\macc@nucleus\rel@kern{0.4}\kern\dimen@}%
      \advance\dimen@0.4\dimexpr\macc@kerna
%Place the combined final kern (-\dimen@) if it is >0 or if a superscript follows:
      \let\final@kern#2%
      \ifdim\dimen@<\z@ \let\final@kern1\fi
      \if\final@kern1 \kern-\dimen@\fi
    \else
      \overline{\rel@kern{-0.6}\kern\dimen@#1}%
    \fi
  }%
  \macc@depth\@ne
  \let\math@bgroup\@empty \let\math@egroup\macc@set@skewchar
  \mathsurround\z@ \frozen@everymath{\mathgroup\macc@group\relax}%
  \macc@set@skewchar\relax
  \let\mathaccentV\macc@nested@a
%The following initialises \macc@kerna and calls \mathaccent:
  \if#31
    \macc@nested@a\relax111{#1}%
  \else
%If the argument consists of more than one symbol, and if the first token is
%a letter, use that letter for the computations:
    \def\gobble@till@marker##1\endmarker{}%
    \futurelet\first@char\gobble@till@marker#1\endmarker
    \ifcat\noexpand\first@char A\else
      \def\first@char{}%
    \fi
    \macc@nested@a\relax111{\first@char}%
  \fi
  \endgroup
}
\makeatother
%%%%%%%%%%%%%%%% END WIDEBAR COMMAND %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




\swapnumbers %% put numbers in front of proclamations
\newtheorem{thm}{Theorem}
\newtheorem*{thm*}{Theorem}
\newtheorem{lem}[thm]{Lemma}
\newtheorem*{lem*}{Lemma}
\newtheorem{prop}[thm]{Proposition}
\newtheorem*{prop*}{Proposition}
\newtheorem{cor}[thm]{Corollary}
\newtheorem*{cor*}{Corollary}
\newtheorem{conj}[thm]{Conjecture}
\newtheorem*{conj*}{Conjecture}

\theoremstyle{definition}
\newtheorem{defn}[thm]{Definition}
\newtheorem*{defn*}{Definition}
\newtheorem{example}[thm]{Example}
\newtheorem*{example*}{Example}
\newtheorem{examples}[thm]{Examples}
\newtheorem*{examples*}{Examples}
\newtheorem{alg}[thm]{Algorithm}
\newtheorem*{alg*}{Algorithm}
%\theoremstyle{remark}
\newtheorem{rmk}[thm]{Remark}
\newtheorem*{rmk*}{Remark}
\newtheorem{rmks}[thm]{Remarks}
\newtheorem*{rmks*}{Remarks}

%%%%%%
\newcommand{\isom}{\mathrel{\cong}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\numberwithin{equation}{section}
%% The following avoids conflict between numbers of proclamations
%% and numbers of equations
\renewcommand{\theequation}{\thesection\alph{equation}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\parskip = 2pt
\allowdisplaybreaks
\renewcommand{\labelenumi}{(\theenumi)} % use round brackets
\renewcommand{\theenumi}{\alph{enumi}} % use alphabetic enumerations


\pagestyle{plain} % suppress the running head - for working document