Related papers: Jantzen filtration of Weyl modules for general lin…

We prove a determinantal type formula to compute the irreducible characters of the general Lie superalgebra $\mathfrak{gl}(m|1)$ in terms of the characters of the symmetric powers of the fundamental representation and their duals. This…

We use enhanced Langlands parameters to obtain a classification for irreducible representations of twisted $p$-adic general linear groups in unramified principal series. We give the definition of standard representations and prove the…

We provide evidence for the existence of a family of generalized Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for (N,k)=(1,10), (2,6),…

For an $n$-fold Kazhdan--Patterson cover or Savin's cover of a general linear group over a non-archimedean local field of residual characteristic $p$ with $\mathrm{gcd}(n,p)=1$, we realize the Gelfand--Graev representation as a Hecke…

We classify all simple bounded highest weight modules of a basic classical Lie superalgebra $\mathfrak g$. In particular, our classification leads to the classification of the simple weight modules with finite weight multiplicities over all…

A class of infinite dimensional Galilean conformal algebra in (2+1) dimensional spacetime is studied. Each member of the class, denoted by \alg_{\ell}, is labelled by the parameter \ell. The parameter \ell takes a spin value, i.e., 1/2, 1,…

Let k be a perfect field of characteristic p>0. When p>2, Fontaine and Laffaille have classified p-divisibles groups and finite flat p-groups over the Witt vectors W(k) in terms of filtered modules. Still assuming p>2, we extend these…

It is well known that $n$-dimensional projective group gives rise to a non-homogenous representation of the Lie algebra $sl(n+1)$ on the polynomial functions of the projective space. Using Shen's mixed product for Witt algebras (also known…

We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations…

Let G be an almost simple, simply connected algebraic group over an algebraically closed field of characteristic p>0. In this paper we restate our conjecture from 1979 on the characters of irreducible modular representations of G so that it…

S. Orlik and M. Strauch have studied locally analytic principal series representation for general $p$-adic reductive groups generalizing an earlier work of P. Schneider for $GL(2)$ and related the condition of irreducibility of such locally…

The polynomial which determine the simplicity of the Kac modules for the restricted Lie superalgebra gl(m,n) is completely determined by a characteristic free approach. Its application on the nonrestricted representation is investigated.

In this paper, we calculate the space $Ext^1_{GL(n)}(L_n(\lambda),L_n(\mu))$, where GL(n) is the general linear group of degree $n$ over an algebraically closed field of positive characteristic, $L_n(\lambda)$ and $L_n(\mu)$ are rational…

We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring $R$), which is assumed to carry an involution of the form $X^*=Y$, $R^*\subseteq R$. We prove…

We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial differential equations defined from a suitable filtration of the Weyl algebra $A_{n}(k)$. This generalizes an important…

We construct a categorification of the modular data associated with every family of unipotent characters of the spetsial complex reflection group $G(d,1,n)$. The construction of the category follows the decomposition of the Fourier matrix…

We show that certain characteristic varieties of a finitely generated module over a given Weyl algebra arising from weighted degree filtrations are equal to the critical cone of some other characteristic varieties. This behaviour of the…

Fix any complex Kac-Moody Lie algebra $\mathfrak{g}$, and Cartan subalgebra $\mathfrak{h}\subset \mathfrak{g}$. We study arbitrary highest weight $\mathfrak{g}$-modules $V$ (with any highest weight $\lambda\in \mathfrak{h}^*$, and let…

We provide the first formulae for the weights of all simple highest weight modules over Kac-Moody algebras. For generic highest weights, we present a formula for the weights of simple modules similar to the Weyl-Kac character formula. For…

We classify all pairs (G,V) with G a closed subgroup in a classical group with natural module V over the complex numbers such that G has the same composition factors on the kth tensor power of V, for a fixed (small) k. In particular, we…