Related papers: Caract\`eres de repr\'esentations de niveau 0

Let $k$ be an infinite finitely generated field of characteristic $p>0$. Fix a separated scheme $X$ smooth, geometrically connected, and of finite type over $k$ and a smooth proper morphism $f:Y\rightarrow X$. The main result of this paper…

Let $G = {\rm U}(2m, {\mathbb F}_{q^2})$ be the finite unitary group, with $q$ the power of an odd prime $p$. We prove that the number of irreducible complex characters of $G$ with degree not divisible by $p$ and with Frobenius-Schur…

In this paper we provide a detailed calculation of the Sweedler cohomology of the algebra of functions on (Z/2)^r, in all degrees, over a field of characteristic 2. The result is strikingly different from the characteristic 0 analog. Then…

Let H denote a semisimple Hopf algebra over an algebraically closed field k of characteristic 0. We show that the degree of any irreducible representation of H whose character belongs to the center of H^* must divide the dimension of H .

In this paper, we get the sharp bound for $|G/O_p(G)|_p$ under the assumption that either $p^2 \nmid \chi(1)$ for all $\chi \in {\rm Irr}(G)$ or $p^2 \nmid \phi(1)$ for all $\phi \in {\rm IBr}_p(G)$. This would settle two conjectures raised…

We establish a character formula for admissible unitary representations of $p$-adic almost algebraic solvable groups and we deduce the Plancherel measure in the unimodular case.

Via counting over finite fields, we derive explicit formulas for the E-polynomials and Euler characteristics of GL(d)- and PGL(d)-character varieties of free groups. We prove a positivity property for these polynomials and relate them to…

Let $G$ be a simple complex Lie group with Weyl group $W$. We give a formula for the character of $W$ on the zero weight space of any finite dimensional representation of $G$. The formula involves partition functions, generalizing Kostant's…

We define and study supercharacters of the classical finite unipotent groups of symplectic and orthogonal types (over any finite field of odd characteristic). We show how supercharacters for groups of those types can be obtained by…

We calculate characters and supercharacters for irreducible, admissible representations of the affine superalgebra sl(2|1) in both the Ramond and Neveu-Schwarz sectors and discuss their modular properties in the special case of level…

We find nice representatives for the 0-dimensional cusps of the degree $n$ Siegel upper half-space under the action of $\Gamma_0(\stufe)$. To each of these we attach a Siegel Eisenstein series, and then we make explicit a result of Siegel,…

This paper addresses Question 1 posed by Dipendra Prasad in his recent problem list: classify all irreducible smooth representations of an unramified reductive p-adic group such that the space of vectors fixed by the pro-unipotent radical…

In this article we extend independent results of Lusztig and H\'ezard concerning the existence of irreducible characters of finite reductive groups, (defined in good characteristic and arising from simple algebraic groups), satisfying a…

We compute the number of points over finite fields of the character stack associated to a compact surface group and a reductive group with connected centre. We find that the answer is a Polynomial On Residue Classes (PORC). The key…

In this paper we study the complex representations of reductive groups over local non-Archimedean fields. We use the building of the reductive group to give upper-bounds for the absolute value of the character of an admissible…

We provide a purely local computation of the (elliptic) twisted (by "transpose-inverse") character of the representation \pi=I(\1) of PGL(3) over a p-adic field induced from the trivial representation of the maximal parabolic subgroup. This…

The category of representations with a strongly typical central character of a basic classical Lie superalgebra is proven to be equivalent to the category of representations of its even part corresponding to an appropriate central…

Let F_0 be a non-archimedean local field of odd residual characteristic and let G be the non quasi-split unramified unitary group in four variables defined over F_0. In this paper, we give a classification of the irreducible smooth…

We discuss implications of the following statement about the representation theory of symmetric groups: every integer appears infinitely often as an irreducible character evaluation, and every nonnegative integer appears infinitely often as…

Character measure is a probability measure on irreducible representations of a semisimple Lie algebra. It appears from the decomposition into irreducibles of tensor power of a fundamental representation. In this paper we calculate the…