Schur Polynomials and Crystal Graphs

dc.contributor.advisor	Leslie, Spencer
dc.contributor.author	Fagan, Lucas
dc.date.accessioned	2021-04-23T14:40:13Z
dc.date.available	2021-04-23T14:40:13Z
dc.date.issued	2021-04-19
dc.department	Mathematics
dc.description.abstract	The Casselman-Shalika formula connects special values of p-adic Whittaker functions to characters of Schur polynomials in type A. We study the structure of the expansion of these Whittaker functions in order to derive new formulas for Schur polynomials. In particular, we give an algorithm for computing the necessary data in order to express the integrals that arise in the expansion. Furthermore, we completely compute all terms in a specific case for GL(4), which gives a new formula for Schur polynomials in four variables.
dc.identifier.uri	https://hdl.handle.net/10161/22610
dc.language.iso	en_US
dc.subject	Schur polynomials
dc.subject	Representation theory
dc.subject	p-adic representation theory
dc.title	Schur Polynomials and Crystal Graphs
dc.type	Honors thesis
duke.embargo.months	0

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