Related papers: Kato's irreducibility criterion for Kac-Moody grou…

It is shown, using the Wakimoto representation, that the level zero SU(2) Kac-Moody conformal field theory is topological and can be obtained by twisting an N=2 superconformal theory. Expressions for the associated N=2 superconformal…

For a split Kac-Moody group G over an ultrametric field K, S. Gaussent and the author defined an ordered affine hovel on which the group acts; it generalizes the Bruhat-Tits building which corresponds to the case when G is reductive. This…

We provide new local characterizations of Hida families of Siegel modular forms with genus two arising from automorphic inductions (stable Yoshida lifts), analogous to the characterizations of Hida families of CM modular forms provided by…

A theorem of Kazhdan and Lusztig establishes an equivalence between the category of G(CO)-integrable representations of the Kac-Moody algebra \hat{g}_{-\kappa} at a negative level -\kappa and the category \Rep_q(G) of (algebraic)…

We give a general lower bound on the rank of matrices of the form $\rho(h) - I$ with $\rho : G \rightarrow GL({\mathbb F}^n)$ an irreducible representation of a finite group $G$. The main tool in the proof is a (strengthening) of a…

First, we prove the Kac-Wakimoto conjecture on modular invariance of characters of exceptional affine W-algebras. In fact more generally we prove modular invariance of characters of all lisse W-algebras obtained through Hamiltonian…

We give new criteria for the irreducibility of parabolic induction on the general linear group and its inner forms over a local non-archimedean field. In particular, we give a necessary and sufficient condition when the inducing data is of…

In this paper we view pro-$p$ Iwahori subgroups $I$ as rigid analytic groups $\Bbb{I}$ for large enough $p$. This is done by endowing $I$ with a natural $p$-valuation, and thereby generalizing results of Lazard for $\text{GL}_n$. We work…

For an arithmetical scheme X, K. Kato introduced a certain complex of Gersten-Bloch-Ogus type whose component in degree a involves Galois cohomology groups of the residue fields of all the points of X of dimension a. He stated a conjecture…

We consider the Iwahori-Hecke algebra associated to an almost split Kac-Moody group $G$ (affine or not) over a nonarchimedean local field $K$. It has a canonical double-coset basis $(T_{\mathbf w})_{\mathbf w\in W^+}$ indexed by a…

We consider the problem of representing the Kac-Moody algebra $\mathfrak{g}(N)$ specified by an $r\times r$ indecomposable generalised Cartan matrix $N$ as vector fields on the torus ${{\bb C}^*}^r$. It is shown that, if the representations…

This is the announcement and partly the review of our results about classification of Lorentzian Kac-Moody algebras of the rank three. One of our results gives the classification of Lorentzian Kac-Moody algebras with denominator identity…

We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model.…

In a recent article, D. Kazhdan and A. Yom Din conjectured the validity of an asymptotic form of Schur's orthogonality for tempered irreducible unitary representations of semisimple groups defined over local fields. In the non-Archimedean…

We establish a new spectral criterion for Kazhdan's property $(T)$ which is applicable to a large class of discrete groups defined by generators and relations. As the main application, we prove property $(T)$ for the groups $EL_n(R)$, where…

The main result of the paper establishes the irreducibility of a large family of nonzero central charge induced modules over Affine Lie algebras for any non standard parabolic subalgebra. It generalizes all previously known partial results…

A conjecture of Kac states that the polynomial counting the number of absolutely indecomposable representations of a quiver over a finite field with given dimension vector has positive coefficients and furthermore that its constant term is…

In conformal field theories, when the conformal symmetry is enhanced by a global Lie group symmetry, the original Virasoro algebra can be extended to Kac-Moody algebra. In this paper, we extend the lattice construction of the Kac-Moody…

This article establishes a geometric Satake equivalence for affine Kac-Moody groups as an equivalence of abelian semisimple categories over algebraically closed fields. We define a well-behaved category of equivariant sheaves on the double…

We construct a map from the classifying space of a discrete Kac-Moody group over the algebraic closure of the field with p elements to the classifying space of a complex topological Kac-Moody group and prove that it is a homology…