Related papers: Graded decomposition numbers for cyclotomic Hecke …

Let H be a graded Hecke algebra with complex deformation parameters and Weyl group W. We show that the Hochschild, cyclic and periodic cyclic homologies of H are all independent of the parameters, and compute them explicitly. We use this to…

We investigate integral forms of simple modules of symmetric groups over fields of characteristic $0$ labelled by hook partitions. Building on work of Plesken and Craig, for every odd prime $p$, we give a set of representatives of the…

Jensen, Su, and Yang described the projective indecomposable modules of the $0$-Schur algebra $\mathbf{S}_0(n,r)$ using its geometric realization. In this paper, the simple modules of $\mathbf{S}_0(n,r)$ are identified by computing the tops…

We show that the quiver Hecke superalgebras and their cyclotomic quotients provide a supercategorification of quantum Kac-Moody algebras and their integrable highest weight modules.

Assuming the Riemann hypothesis for $L$-functions attached to primitive Dirichlet characters, modular cusp forms, and their tensor products and symmetric squares, we write down explicit finite sets of Hecke operators that span the Hecke…

In this note, we study the twisted Jacquet modules of sub-quotients of principal series representations of ${\rm GL}_2(D)$ where $D$ is a division algebra over a non-archimedean local field $F$. We begin with a proof of a conjecture due to…

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…

We generalize a result of Galatius and Venkatesh which relates the graded module of cohomology of locally symmetric spaces to the graded homotopy ring of the derived Galois deformation rings, by removing certain assumptions, and in…

We present an application of the program of groupoidification leading up to a sketch of a categorification of the Hecke algebroid --- the category of permutation representations of a finite group. As an immediate consequence, we obtain a…

We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…

Schur modules give the irreducible polynomial representations of the general linear group $\mathrm{GL}_t$. Viewing the symmetric group $\mathfrak{S}_t$ as a subgroup of $\mathrm{GL}_t$, we may restrict Schur modules to $\mathfrak{S}_t$ and…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

We describe a graded extension of the usual Hecke algebra: it acts in a graded fashion on the cohomology of an arithmetic group $\Gamma$. Under favorable conditions, the cohomology is freely generated in a single degree over this graded…

In this paper we study homological properties of modules over an affine Hecke algebra H. In particular we prove a comparison result for higher extensions of tempered modules when passing to the Schwartz algebra S, a certain topological…

Let n be a positive integer and let Sigma_n be the symmetric group of degree n. Let S^lambda be the Specht module for Sigma_n corresponding to a partition lambda of n, defined over a field F of odd characteristic. We find the indecomposable…

We estimate the number of possible types degree patterns of $k$-lacunary polynomials of degree $t < p$ which split completely modulo $p$. The result is based on a combination of a bound on the number of zeros of lacunary polynomials with…

We present some blocks of Ariki-Koike algebras $\mathcal{H}_{n,r}$ for which the decomposition matrices are independent of the characteristic of the underlying field. We complete the description of the graded decomposition numbers for…

We consider the core blocks corresponding to the Hecke algebras of type B over a field of arbitrary characteristic. To each core block B, we associate two non-negative integers which determine the indexing of the Specht modules and simple…

In this paper, we study extensions of graded affine Hecke algebra modules. In particular, based on an explicit projective resolution on graded affine Hecke algebra modules, we prove a duality result for Ext-groups. This duality result with…

We explore the structure of the derived spherical Hecke algebra of a $p$-adic group, a graded associative algebra whose degree $0$ subalgebra is the classical spherical Hecke algebra. Working with $\mathbb Z/ p^a$ coefficients, we establish…