Daniel Bump, Colored Bosonic Lattice Models and Matrix Coefficients

Solvable Lattice Models Seminar

Abstract: Colored bosonic lattice models were studied and applied by Borodin and Wheeler. We will consider particular bosonic models whose theory is strikingly parallel to the fermionic models described by Brubaker, Buciumas, Bump and Gustafsson, who applied them to study Whittaker functions of GL_r(F) over a nonarchimedean local field. The many parallels with the BBBG theory include a monochrome factorization, a local lifting property, and very similar R-matrices; indeed the R-matrices are the same except for a very minor change which reflects the quantum group U_q(sl_{r+1}) in the bosonic models, versus U_q(gl(r|1)) in the fermionic models. We will show that the partition functions of the bosonic models are equal to matrix coefficients of principal series representations of GL_r(F), where F is a nonarchimedean local field. We will also explain the relationship with nonsymmetric Hall-Littlewood polynomials. This is joint work with Slava Naprienko.