Related papers: On induction of class functions

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp.…

Let $G$ be a connected semisimple Lie group with a finite center, with a maximal compact subgroup $K$. There are two general methods to construct representations of $G$, namely, ordinary parabolic induction and cohomological parabolic…

We use intuitive results from algebraic topology and intersection theory to clarify the pullback action on cohomology by compositions of rational maps. We use these techniques to prove a simple sufficient criterion for functoriality of a…

For a finite group scheme, the subadditive functions on finite dimensional representations are studied. It is shown that the projective variety of the cohomology ring can be recovered from the equivalence classes of subadditive functions.…

We study the compatibility of the formal degree conjecture and the parabolic induction process in the simplest nontrivial case for quasi-split $p$-adic groups. For a generic discrete series $\pi$ induced from an irreducible supercuspidal…

In this work we study the induction theory for Hopf group coalgebra. To reach this goal we define a substructure B of a Hopf group coalgebra $H$, called subHopf group coalgebra. Also, we introduced the definition of Hopf group suboalgebra…

Let $M$ be an irreducible projective variety over an algebraically closed field $k$ of characteristic zero equipped with an action of a group $\Gamma$. Let $E_G$ be a principal $G$--bundle over $M$, where $G$ is a connected reductive…

This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If $RG$ is a group ring, where $R$ is commutative and $S$ is a set of generators of $G$ then necessary and sufficient…

We prove a classification of additive polynomial superfunctors, which allows us to compute some extensions of a superfunctor of the form $F \circ A$ where $F$ is a classical polynomial functor and $A$ is additive. We get a formula which…

Let $\Gamma$ be a finite group acting linearly on a vector space $V$. We compute the Lie algebra cohomology of the Lie algebra of $\Gamma$-invariant formal vector fields on $V$. We use this computation to define characteristic classes for…

Let $G$ be a finite group. To any family $\mathscr{F}$ of subgroups of $G$, we associate a thick $\otimes$-ideal $\mathscr{F}^{\mathrm{Nil}}$ of the category of $G$-spectra with the property that every $G$-spectrum in…

We consider the class $PW(\mathbb R^n)$ of functions in $L^2(\mathbb R^n)$, whose Fourier transform has bounded support. We obtain a description of continuous maps $\varphi : \mathbb R^m\rightarrow\mathbb R^n$ such that $f\circ\varphi\in…

Let $G$ be a group hyperbolic relative to a finite collection of subgroups $\mathcal P$. Let $\mathcal F$ be the family of subgroups consisting of all the conjugates of subgroups in $\mathcal P$, all their subgroups, and all finite…

Inductive algebras for the irreducible unitary representations of the universal cover of the group of unimodular two by two matrices are classified. The classification of homogeneous shift operators is obtained as a direct consequence. This…

For an algebraic stack $\sX$ flat and of finite presentation over a scheme $S$, we introduce various notions of {\em relative connected components} and {\em relative irreducible components}. The main distinction between these notions is…

We introduce the representation category $\mathscr{C}({\bf G})$ for a connected reductive algebraic group ${\bf G}$ which is defined over a finite field $\mathbb{F}_q$ of $q$ elements. We show that this category has many good properties for…

We introduce a reducibility on classes of structures, essentially a uniform enumeration reducibility. This reducibility is inspired by the Friedman-Stanley paper on using Borel reductions to compare classes of countable structures. This…

This paper is about the reduced group C*-algebras of real reductive groups, and about Hilbert C*-modules over these C*-algebras. We shall do three things. First we shall apply theorems from the tempered representation theory of reductive…

In this paper, we discuss positive maps induced by (irreducibly) covariant linear operators for finite groups. The application of group theory methods allows deriving some new results of a different kind. In particular, a family of…

Let $A \cong k\langle X \rangle / I$ be an associative algebra. A finite word over alphabet $X$ is $I${\it-reducible} if its image in $A$ is a $k$-linear combination of length-lexicographically lesser words. An {\it obstruction} in a…