Algebra Seminar: Jing -- Quantum Littlewood correspondences

Naihuan Jing (NC State University) will be speaking in the algebra seminar.  We will go
out for lunch after the talk---all are welcome to join! 

When: 12-1pm Friday April 24 

Where: Carslaw 175 

Title: Quantum Littlewood correspondences 

Abstract: In the 1940s Littlewood formulated three fundamental correspondences parallel
to the Schur-Weyl duality.  I will talk about how to introduce the quantum version of
quantum immanants and the quantum Littlewood correspondences between quantum immanants
and Schur functions for the quantum general linear group and the Heck algebra.  Via the
correspondences, we have found an exact relationship between the Gelfand-Tsetlin basis
of $U_q(gl(n))$ and Young's orthonormal basis for the Hecke algebra.  This leads to a
trace formula for the quantum immanants that has settled the generalization problem of
$q$-analog of Kostant's formula for $\lambda$-immanants.  As applications, we also
derive general $q$-Littlewood-Merris-Watkins identities and $q$-Goulden-Jackson
identities as special cases of the quantum Littlewood correspondence III.  This is joint
work with Jian Zhang.