Related papers: Alvis-Curtis duality, central characters, and real…

We calculate Frobenius-Schur indicator values for some fusion categories obtained from inclusions of finite groups $H\subset G$, where more concretely $G$ is symmetric or alternating, and $H$ is a symmetric, alternating or cyclic group. Our…

In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras of reductive algebraic groups over a field of large positive characteristic. The equivariance is with…

We give two generalizations of the Alvis-Curtis duality for Hecke algebras: an unequal parameter version for the affine Hecke algebras, based on S.-I. Kato's work, and a relative version for finite Hecke algebras, based on Howlett-Lehrer's…

We define exact functors from categories of Harish-Chandra modules for certain real classical groups to finite-dimensional modules over an associated graded affine Hecke algebra with parameters. We then study some of the basic properties of…

With a view to determining character values of finite reductive groups at unipotent elements, we prove a number of results concerning inner products of generalised Gelfand-Graev characters with characteristic functions of character sheaves,…

For a classical group over a non-archimedean local field of odd residual characteristic p, we prove that two cuspidal types, defined over an algebraically closed field C of characteristic different from p, intertwine if and only if they are…

Let N be a finite group of odd order and A a finite group that acts on N such that the orders of N and A are coprime. Isaacs constructed a natural correspondence between the set Irr_A(N) of irreducible complex characters invariant under the…

We prove for finite reductive groups $G$ of classical type, that every irreducible character of $L$ extends to its inertia group in $N$, where $L$ is an abelian centraliser of a Sylow $d$-torus $\mathbf S$ of $G$ and $N:=N_G(\mathbf S)$.…

Let $W$ be a finite Coxeter group. It is well-known that the number of involutions in $W$ is equal to the sum of the degrees of the irreducible characters of $W$. Following a suggestion of Lusztig, we show that this equality is compatible…

We apply the ideas of derived algebraic geometry and topological field theory to the representation theory of reductive groups. Our focus is the Hecke category of Borel-equivariant D-modules on the flag variety of a complex reductive group…

The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this…

Let $(G,G')$ be a reductive dual pair of a symplectic group and an orthogonal group over a finite field of odd characteristic. The Howe correspondence establishes a correspondence between a subset of irreducible characters of $G$ and a…

We prove Clifford theoretic results on the representations of finite groups which only hold in characteristic $2$. Let $G$ be a finite group, let $N$ be a normal subgroup of $G$ and let $\varphi$ be an irreducible $2$-Brauer character of…

This is a survey of results and conjectures on mirror symmetry phenomena in the non-Abelian Hodge theory of a curve. We start with the conjecture of Hausel-Thaddeus which claims that certain Hodge numbers of moduli spaces of flat SL(n,C)…

We present a new approach to calculating the higher Frobenius-Schur indicators for the simple modules over the Drinfeld double of a finite group. In contrast to the formula by Kashina-Sommerh{\"a}user-Zhu that involves a sum over all group…

We extend the notion of Frobenius Betti numbers and F-splitting ratio to large classes of finitely generated modules over rings of prime characteristic, which are not assumed to be local. We also prove that the strong F-regularity of a pair…

We develop invariants of the lower central series of free groups through linking of letters, showing they span the rational linear dual of the lower central series subquotients. We build on an approach to Lie coalgebras through operads,…

In an earlier paper [1] it was shown that the Frobenius compound characters for the symmetric groups are related to the irreducible characters by a linear relation that involves a unitriagular coupling matrix that gives the Frobenius…

We show that stable equivalences between Artin algebras without nodes preserve homological data that provide upper bounds for finitistic dimension, and that stable equivalences between Artin algebras with positive $\nu$-dominant dimensions…

Let G be a connected real reductive Lie group acting linearly on a finite dimensional vector space V over R. This action admits a Kempf-Ness function and so we have an associated gradient map. If G is Abelian we explicitly compute the image…