| Title | Publication Details | Abstract | Comments | Download |
| Principal Series Representations of Metaplectic Groups Over Local Fields | Let $G$ be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension $\G$ of $G$ by a cyclic group of order $n$, under some mild tameness assumptions on $n$. In particular, we focus our attention on the development of the theory of principal series representations for $\G$ and applications of this theory. | |||
| Factorial Schur Polynomials and the Six Vertex model | For a particular set of Boltzmann weights and a particular boundary condition for the six vertex model in statistical mechanics, we compute explicitly the partition function and show it to be equal to a factorial Schur function, giving a new proof of a theorem of Lascoux. | If you are one of the people still reading version 1 on the arxiv, this is out of date. | ||
| Metaplectic Whittaker Functions and Crystal Bases | Submitted For Publication. | We study Whittaker functions on nonlinear coverings of simple algebraic groups over a non-archimedean local field. We produce a recipe for expressing such a Whittaker function as a weighted sum over a crystal graph, and show that in type A, these expressions agree with known formulae for the $p$-part of Multiple Dirichlet Series. | ||
| Factorial Grothendieck Polynomials | The Electronic Journal of Combinatorics, 13 (2006), R71. | In this paper, we study Grothendieck polynomials indexed by Grassmannian permutations from a combinatorial viewpoint. We introduce the factorial Grothendieck polynomials which are analogues of the factorial Schur functions, study their properties, and use them to produce a generalisation of a Littlewood-Richardson rule for Grothendieck polynomials. | 1. The published version is more polished than the arxiv version, so you should look at that. For example the proof of the Main Theorem is not quite complete in the arxiv version. 2. Reference [5] should probably in places refer to arXiv:hep-th/9306005. |