Higher Kazhdan projections for one relator groups

Modular functoriality for finite groups

We develop an extension of Deligne--Lusztig theory to certain (possibly infinite type) disconnected reductive groups arising from the special fibers of point stabilizers in the Bruhat--Tits building, which we call \emph{paraductive}. We then compute explicit lower bounds for the Tate cohomology of representations of pa...

Kloosterman sheaves and Bessel functions for generic principal series of finite groups

Let $G$ be a quasi-split reductive group over a finite field and let $\^G$ be the Langlands dual group. Assuming the derived subgroup of $G$ is almost simple, we use techniques from the geometric Langlands program to relate special values of Bessel functions for generic principal series representations of $G$ to the tr...

Equivariant spaces of matrices of constant corank one

We classify all irreducible G$G$ ‐equivariant subspaces of Hom(V1,V2)$\operatorname{Hom}(V_1,V_2)$ of constant corank one, where G$G$ is a reductive group over an algebraically closed field of characteristic zero and Vi$V_i$ are irreducible representations. We give explicit necessary and sufficient conditions on the hi...

Lusztig’s partition and sheets

Splitting the Matroid Determinant

The principal matroid determinant $E_L$ of a linear space $L \subseteq \mathbb{P}^n$ has been introduced in recent work by Matsubara-Heo and Telen. In this paper, we give the complete factorization of this polynomial into its irreducible components, proving a conjecture of the aforementioned authors. Our methods rely o...

Double coset Schur rings and diagonal subgroups

We investigate the structure of Schur rings arising from group triples $(G, H, K)$, where $K \trianglelefteq H \leq G$, building on foundational work by Brender and Travis. Central to our approach is the interplay between Schur rings and (strong) Gelfand pairs. We introduce certain double coset algebras, and illustrate...