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Twisted Weyl Group Multiple Dirichlet Series Over the Rational Function Field

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dc.contributor.advisorPaul E. Gunnells
dc.contributor.advisorSiman Wong
dc.contributor.advisorFarshid Hajir
dc.contributor.authorFriedlander, Holley Ann
dc.contributor.departmentUniversity of Massachusetts Amherst
dc.date2023-09-23T08:32:21.000
dc.date.accessioned2024-04-26T19:54:43Z
dc.date.available2024-04-26T19:54:43Z
dc.date.issued2013-09-01
dc.description.abstractLet K be a global field. For each prime p of K, the p-part of a multiple Dirichlet series defined over K is a generating function in several variables for the p-power coefficients. Let _ be an irreducible, reduced root system, and let n be an integer greater than 1. Fix a prime power q 2 Z congruent to 1 modulo 2n, and let Fq(T) be the field of rational functions in T over the finite field Fq of order q. In this thesis, we examine the relationship between Weyl group multiple Dirichlet series over K = Fq(T) and their p-parts, which we define using the Chinta-Gunnells method [10]. Our main result shows that Weyl group multiple Dirichlet series of type _ over Fq(T) may be written as the finite sum of their p-parts (after a certain variable change), with “multiplicities" that are character sums. This result gives an analogy between twisted Weyl group multiple Dirichlet series over the rational function field and characters of representations of semi-simple complex Lie algebras associated to _. Because the p-parts and global series are closely related, the result above follows from a series of local results concerning the p-parts. In particular, we give an explicit recurrence relation on the coefficients of the p-parts, which allows us to extend the results of Chinta, Friedberg, and Gunnells [9] to all _ and n. Additionally, we show that the p-parts of Chinta and Gunnells [10] agree with those constructed using the crystal graph technique of Brubaker, Bump, and Friedberg [4, 5] (in the cases when both constructions apply).
dc.description.degreeDoctor of Philosophy (PhD)
dc.description.departmentMathematics
dc.identifier.doihttps://doi.org/10.7275/dvk2-0b68
dc.identifier.urihttps://hdl.handle.net/20.500.14394/39290
dc.relation.urlhttps://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1836&context=open_access_dissertations&unstamped=1
dc.source.statuspublished
dc.subjectMathematics
dc.titleTwisted Weyl Group Multiple Dirichlet Series Over the Rational Function Field
dc.typedissertation
dc.typearticle
dc.typedissertation
digcom.contributor.authorisAuthorOfPublication|email:holleyf85@gmail.com|institution:University of Massachusetts Amherst|Friedlander, Holley Ann
digcom.identifieropen_access_dissertations/831
digcom.identifier.contextkey4864455
digcom.identifier.submissionpathopen_access_dissertations/831
dspace.entity.typePublication
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