Related papers: On integral $\mathrm{Ext^2}$ between certain Weyl …

In this note we determine when is an induced module H^0_G(\lambda), corresponding to a dominant integral highest weight \lambda of the general linear supergroup G=GL(m|n) irreducible. Using the contravariant duality given by the supertrace…

Equivariant map algebras are Lie algebras of algebraic maps from a scheme (or algebraic variety) to a target finite-dimensional Lie algebra (in the case of the current paper, we assume the latter is a simple Lie algebra) that are…

We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and Symplectic groups.…

Degeneration of modules is usually defined geometrically, but due to results of Zwara and Riedtmann we can also define it in terms of exact sequences. This definition also works over fields that are not algebraically closed. Let $k$ be a…

We study the Ext-algebra of the direct sum of all parabolic Verma modules in the principal block of the Bernstein-Gelfand-Gelfand category O for the hermitian symmetric pair $(\mathfrak{gl}_{n+m}, \mathfrak{gl}_{n} \oplus \mathfrak{gl}_m)$…

We study the Weyl groups of hyperbolic Kac-Moody algebras of `over-extended' type and ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K=R,C,H,O, respectively. A crucial role is played by integral…

Let $k$ and $N$ be positive integers with $k\ge2$ even. In this paper we give general explicit upper-bounds in terms of $k$ and $N$ from which all the residual representations $\bar{\rho}_{f,\lambda}$ attached to non-CM newforms of weight…

Let g be the finite dimensional Witt algebra W(1,1) over an algebraically closed field of characteristic p > 3. It is well known that all simple W(1,1)-modules are finite dimensional. Each simple module admits a character \chi in g^*. Given…

The Newell-Littlewood numbers $N_{\mu,\nu,\lambda}$ are tensor product multiplicities of Weyl modules for classical Lie groups, in the stable limit. For which triples of partitions $(\mu,\nu,\lambda)$ does $N_{\mu,\nu,\lambda}>0$ hold? The…

Let ${\cal F}\_\lambda(S^1)$ be the space of tensor densities of degree (or weight) $\lambda$ on the circle $S^1$. The space ${\cal D}^k\_{\lambda,\mu}(S^1)$ of $k$-th order linear differential operators from ${\cal F}\_\lambda(S^1)$ to…

In this work, we investigate the approach via flipclasses to the Combinatorial Invariance Conjecture for Kazhdan--Lusztig polynomials of all Coxeter groups. We prove the combinatorial invariance of Kazhdan--Lusztig…

We define Schur categories, $\Gamma^d \mathcal C$, associated to a $\Bbbk$-linear category $\mathcal C$, over a commutative ring $\Bbbk$. The corresponding representation categories, $\mathbf{rep}\, \Gamma^d\mathcal C$, generalize…

We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser {\it et al.}, and S. Majid. For any finite Weyl group $W$ we consider the subalgebra generated by flat…

Let B be a reductive Lie subalgebra of a semi-simple Lie algebra of the same rank both over the complex numbers. To each finite dimensional irreducible representation $V_\lambda$ of F we assign a multiplet of irreducible representations of…

Weyl modules were originally defined for affine Lie algebras by Chari and Pressley in \cite{CP}. In this paper we extend the notion of Weyl modules for a Lie algebra $\mathfrak{g} \otimes A$, where $\mathfrak{g}$ is any Kac-Moody algebra…

The aim of the article is to show that there are many finite extensions of arithmetic groups which are not residually finite. Suppose $G$ is a simple algebraic group over the rational numbers satisfying both strong approximation, and the…

Extended affine Weyl groups are the Weyl groups of extended affine root systems. Finite presentations for extended affine Weyl groups are known only for nullities $\leq 2$, where for nullity 2 there is only one known such presentation. We…

The rational Cherednik algebra $\HH$ is a certain algebra of differential-reflection operators attached to a complex reflection group $W$. Each irreducible representation $S^\lambda$ of $W$ corresponds to a standard module $M(\lambda)$ for…

This paper considers Weyl modules for a simple, simply connected algebraic group over an algebraically closed field $k$ of positive characteristic $p\not=2$. The main result proves, if $p\geq 2h-2$ (where $h$ is the Coxeter number) and if…

Let n geq 1, let lambda be a partition of n, let mu be a partition arising from lambda by a downwards shift of two boxes situated at the bottom of a column. We give a formula for a ZS_n-linear morphism of order m between the corresponding…