A Plethysm Formula on the Characteristic Map of Induced Linear Characters from Un(𝔽q) to GL(𝔽q)

New Branching Rules Induced by Plethysm * B. Fauser

We derive group branching laws for formal characters of subgroups Hπ of GL(n) leaving invariant an arbitrary tensor T π of Young symmetry type π where π is an integer partition. The branchings GL(n) ↓ GL(n − 1) , GL(n) ↓ O(n) and GL(2n) ↓ Sp(2n) fixing a vector vi , a symmetric tensor gij = gji and an antisymmetric tensor fij = −fji , respectively, are obtained as special cases. All new branchi...

Plethysm of Schur Functions and Irreducible Polynomial Representations of the Complex General Linear Group

We show the intimate connection Schur functions have with the irreducible polynomial representations of GL(n,C). Following Schur’s thesis, in Section 1, we prove that the characters of these representations are given by Schur functions. In the second section, we elaborate on how a specific combinatorial operation on symmetric functions called plethysm gives the characters of the composition of ...

On Characters of Irreducible Unitary Representations of General Linear Groups

Founding harmonic analysis on classical simple complex groups, I.M. Gelfand and M.A. Naimark in their classical book [GN] posed three basic questions: unitary duals, characters of irreducible unitary representations and Plancherel measures. In the case of reductive p-adic groups, the only series of reductive groups where unitary duals are known are general linear groups. In this paper we reduce...

Shifted convolution and the Titchmarsh divisor problem over 𝔽q[t].

In this paper, we solve a function field analogue of classical problems in analytic number theory, concerning the autocorrelations of divisor functions, in the limit of a large finite field.

Correction to 'Shifted convolution and the Titchmarsh divisor problem over 𝔽q[t]'.