Related papers: Springer representations on the Khovanov Springer …

For any reductive group G and a parabolic subgroup P with its Levi subgroup L, the first author in [Ku2] introduced a ring homomorphism $ \xi^P_\lambda: Rep^\mathbb{C}_{\lambda-poly}(L) \to H^*(G/P, \mathbb{C})$, where $…

This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturally the classification of irreducible square integrable representations modulo cuspidal data…

Let $G$ be a finite simple group of Lie type, and let $\pi_G$ be the permutation representation of $G$ associated with the action of $G$ on itself by conjugation. We prove that every irreducible representation of $G$ is a constituent of…

In the Vershik-Okounkov approach to the complex irreducible representations of $S_n$ and $G\sim S_n$ we parametrize the irreducible representations and their bases by spectral objects rather than combinatorial objects and then, at the end,…

The tensor square conjecture states that for $n \geq 10$, there is an irreducible representation $V$ of the symmetric group $S_n$ such that $V \otimes V$ contains every irreducible representation of $S_n$. Our main result is that for large…

Results are obtained on extending flat vector bundles or equivalently general representations from the fundamental group of S, a connected subsurface of the connected boundary of a compact, connected, oriented 3-dimensional manifold, to the…

Denote the virtual cohomological dimension of SL_n(Z) by t=n(n-1)/2. Let St denote the Steinberg module of SL_n(Q) tensored with Q. Let Sh_* denote the sharbly resolution of the Steinberg module St. By Borel-Serre duality, the…

Let $K$ be a non-archimedean local field of residual characteristic $p\neq 2$. Let $G$ be a connected reductive group over $K$, let $\theta$ be an involution of $G$ over $K$, and let $H$ be the connected component of $\theta$-fixed subgroup…

This paper aims at the following results: \begin{enumerate} \item The class of all $*$-regular rings forms a variety. \item A subdirectly irreducible $*$-regular ring $R$ is faithfully representable (i.e. isomorphic to a subring of an…

In the first part of the paper we defined and studied a binary operation on the set of irreducible components of Lusztig's nilpotent varieties of a quiver. For type $A$ we conjecture, following Geiss and Schr\"oer, that this operation is…

We introduce generalized Hessenberg varieties and establish basic facts. We show that the Tymoczko action of the symmetric group $S_n$ on the cohomology of Hessenberg varieties extends to generalized Hessenberg varieties and that natural…

Let $H^*(\calB_e)$ be the cohomology of the Springer fibre for the nilpotent element $e$ in a simple Lie algebra $\g$, on which the Weyl group $W$ acts by the Springer representation. Let $\Lambda^i V$ denote the $i$th exterior power of the…

A permutation is called covexillary if it avoids the pattern $3412$. We construct an open embedding of a covexillary matrix Schubert variety into a Grassmannian Schubert variety. As applications of this embedding, we show that the…

We study maximal representations of surface groups $\rho:\pi_1(\Sigma)\to\mathrm{SO}_0(2,n+1)$ via the introduction of $\rho$-invariant pleated surfaces inside the pseudo-Riemannian space $\mathbb{H}^{2,n}$ associated to maximal geodesic…

The moduli space of twisted stable maps into the stack $B(\Z/m\Z)^2$ carries a natural $S_n$-action and so its cohomology may be decomposed into irreducible $S_n$-representations. Working over $\Spec \Z[1/m]$ we show that the alternating…

We show a Springer type theorem for the variety of parabolic subgroups of type $1,2,6$ for all groups of type $E_6$. As far as we know this gives the first example for the validity of the Springer theorem for projective homogeneous…

We study the algebraic properties of the series $\mathrm{K}_n$ of semigroups, which is inspired by \cite{Ki} and has origins in convexity theory. In particular, we describe Green's relations on $\mathrm{K}_n$, prove that there exists a…

We introduce a variant of the much-studied $Lie$ representation of the symmetric group $S_n$, which we denote by $Lie_n^{(2)}.$ Our variant gives rise to a decomposition of the regular representation as a sum of {exterior} powers of modules…

For strongly invertible knots, we define an involutive version of Khovanov homology, and from it derive a pair of integer-valued invariants $(\underline{s}, \bar{s})$, which is an equivariant version of Rasmussen's $s$-invariant. Using…

Let G denote a complex, semisimple, simply-connected group. We identify the equivariant quantum differential equation for the cotangent bundle to the flag variety of G with the affine Knizhnik-Zamolodchikov connection of Cherednik and…