7 papers
Linearly Independent Products of Rectangularly Complementary Schur Functions
Michael Kleber
Fix a rectangular Young diagram R, and consider all the products of Schur functions s(mu) s(mu^c), where mu and mu^c run over all (unordered) pairs of partitions which are compleme…
Symmetric Functions and Representations of Quantum Affine Algebras
Vyjayanthi Chari, Michael Kleber
We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families…
Embeddings of Schur functions into types B/C/D
Michael Kleber
We consider the problem of embedding the semi-ring of Schur-positive symmetric polynomials into its analogue for the classical types . If we preserve highest weights and add…
Bijective proofs for Schur function identities which imply Dodgson's condensation formula and Plücker relations
Markus Fulmek, Michael Kleber
We present a ``method'' for bijective proofs for determinant identities, which is based on translating determinants to Schur functions by the Jacobi--Trudi identity. We illustrate…
Tournament Sequences and Meeussen Sequences
Matthew Cook, Michael Kleber
A "tournament sequence" is an increasing sequence of positive integers (t_1,t_2,...) such that t_1=1 and t_{i+1} <= 2 t_i. A "Meeussen sequence" is an increasing sequence of positi…
Plucker Relations on Schur Functions
Michael Kleber
We present a set of algebraic relations among Schur functions which are a multi-time generalization of the ``discrete Hirota relations'' known to hold among the Schur functions of…