We give a simple combinatorial proof of Ram’s rule for computing the characters of the Hecke Algebra. We also establish a relationship between the characters of the Hecke algebra and the Kronecker product of two irreducible representations of the Symmetric Group which allows us to give new combinatorial interpretations to the Kronecker product of two Schur functions evaluated at a Schur functio...

Let Eλ be the Hilbert space spanned by the eigenfunctions of the nonEuclidean Laplacian associated with a positive discrete eigenvalue λ. In this paper, the trace of Hecke operators Tn acting on the space Eλ is computed for Hecke congruence subgroups Γ0(N) of non-square free level. This extends the computation of Conrey-Li [2], where only Hecke congruence subgroups Γ0(N) of square free level N ...

‎We show that for all normalized Hecke eigenforms $f$‎ ‎with weight one and of CM type‎, ‎the number $(f,f)$ where $(cdot‎, ‎cdot )$ denotes‎ ‎the Petersson inner product‎, ‎is a linear form in logarithms and‎ ‎hence transcendental‎.

Let Γ be a lattice in a locally compact group G. In earlier work, we used KKtheory to equip the K-groups of any Γ-C∗-algebra on which the commensurator of Γ acts with Hecke operators. When Γ is arithmetic, this gives Hecke operators on the K-theory of certain C ∗-algebras that are naturally associated with Γ. In this paper, we first study the topological Ktheory of the arithmetic manifold assoc...

The well-known R-polynomials in Z[q], which appear in Hecke algebra computations, are closely related to certain modified R-polynomials in N[q] whose coefficients have simple combinatorial interpretations. We generalize this second family of polynomials, providing combinatorial interpretations for expressions arising in a much broader class of computations. In particular, we extend results of B...

Based on a recent result of the author and A.Mathas, we prove that Uno’s conjecture on representation types of Hecke algebras is true for all Hecke algebras of classical type.

We define Hecke operators on vector valued modular forms transforming with the Weil representation associated to a discriminant form. We describe the properties of the corresponding algebra of Hecke operators and study the action on modular forms.

This paper is concerned with the modular representation theory of the affine Hecke-Clifford superalgebra, the cyclotomic Hecke-Clifford superalgebras, and projective representations of the symmetric group. Our approach exploits crystal graphs of affine Kac-Moody algebras.