Rotating restricted Schur polynomials

Complexity of tropical Schur polynomials

We study the complexity of computation of a tropical Schur polynomial Tsλ where λ is a partition, and of a tropical polynomial Tmλ obtained by the tropicalization of the monomial symmetric function mλ. Then Tsλ and Tmλ coincide as tropical functions (so, as convex piece-wise linear functions), while differ as tropical polynomials. We prove the following bounds on the complexity of computing ove...

Traces, Cauchy identity, Schur polynomials

Such identities arise in Rankin-Selberg integral representations of L-functions. For GL2, a naive, direct computation is sufficient. However, for general GLn and other higher-rank groups, direct computation is inadequate. Further, connecting local Rankin-Selberg computations to Schur functions usefully connects these computations to the Shintani-Casselman-Shalika formulas for spherical p-adic W...

Connections between real Schur polynomials and half order complex Schur polynomials

(where a, , , , = a _ , = 0). Suppose that [possibly after replacement of f ( s ) by f ( s ) l either a,, > 0 for i = 0, 1,. . . , n or a , > 0 , a,, > 0 and a, , , , > 0 for i = 0, 1,. . . , n 1. Then if any of f ( s ) , f , (s) and f,(s) has all zeros in Re[sl < 0, the other two polynomials have this property. In this work, we shall indicate how a parallel result can be obtained for discrete-...

A Determinantal Formula for Supersymmetric Schur Polynomials

We derive a new formula for the supersymmetric Schur polynomial sλ(x/y). The origin of this formula goes back to representation theory of the Lie superalgebra gl(m/n). In particular, we show how a character formula due to Kac and Wakimoto can be applied to covariant representations, leading to a new expression for sλ(x/y). This new expression gives rise to a determinantal formula for sλ(x/y). I...

Schubert Polynomials and Skew Schur Functions