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\begin{center}

  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2021--22--B term}\\[0.2\baselineskip]

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\begin{description}
  \item[Course Name]
    Introduction to representation theory of groups

  \item[Course Number]
    \LRE{201‭.1‭.0511}

  \item[Course web page]\mbox{}\\
    \url{https://www.math.bgu.ac.il//en/teaching/spring2022/courses/representation-theory}

  \item[Lecturer]
    Prof. Inna  Entova-Aizenbud,
    \nolinkurl{<entova@bgu.ac.il>},
    Office 312

\item[Office Hours]
  \url{https://www.math.bgu.ac.il/en/teaching/hours}
\end{description}

\section*{Abstract}




\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}






\section*{Course topics}

\begin{enumerate}
\item{} Introduction: Actions of groups on sets. Induced linear actions. Multilinear algebra.
\item{} Representations of groups, direct sum. Irreducible representations, semi-simple representations. Schur's lemma. Irreducible representations of finite abelian groups. Complete reducibility, Machke's theorem.
\item{} Equivalent representations. Morphisms between representations. The category of representations of a finite group. A description using the group ring. Multilinear algebra of representations: dual representation, tensor product (inner and outer).
\item{} Decomposition of the regular representation into irreducible representations. The number of irreducibles is equal to the number of conjugacy classes. Matrix coefficients, characters, orthogonality.
\item{} Harmonic analysis: Fourier transform on finite groups and the non-commutative Fourier transform.
\item{} Frobenius divisibility and Burnside $p^aq^b$ theorem.
\item{} Constructions of representations: induced representations. Frobenius reciprocity. The character of induced representation. Mackey's formula. Mackey's method for representations of semi-direct products.
\item{} Induction functor: as adjoint to restrictions, relation to tensor product. Restriction problems, multiplicity problems, Gelfand pairs and relative representation theory.
\item{} Examples of representations of specific groups: $SL_2$ over finite fields, Icosahedron group, Symmetric groups.
\item{} Artin and Brauer Theorems on monomial representations
\end{enumerate}

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