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Metaplectic Ice for Cartan Type C.

ProQuest Information and Learning Co.

Metaplectic Ice for Cartan Type C.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Metaplectic Ice for Cartan Type C./
Author:	Gray, Nathan Tyler.
Description:	1 online resource (86 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:	Dissertation Abstracts International79-02B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355319019

Metaplectic Ice for Cartan Type C.
Gray, Nathan Tyler.

Metaplectic Ice for Cartan Type C. - 1 online resource (86 pages)

Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

We use techniques from statistical mechanics to give evidence for new formulas for nonarchimedean metaplectic Whittaker functions, arising in the local theory of automorphic forms. We study a particular variation/generalization of the six-vertex model of type C having domain-wall boundary conditions dependent on a given integer partition lambda of length at most r, where r is a fixed positive integer. More precisely, we examine a planar, non-nested, U-turn model whose partition function Z lambda is related to characters of the symplectic group Sp(2 r, C).

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355319019Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Metaplectic Ice for Cartan Type C.
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020 $a 9780355319019
035 $a (MiAaPQ)AAI10287518
035 $a (MiAaPQ)umn:18229
035 $a AAI10287518
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Gray, Nathan Tyler. $3 1180772
245 1 0 $a Metaplectic Ice for Cartan Type C.
264 0 $c 2017
300 $a 1 online resource (86 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
500 $a Adviser: Benjamin Brubaker.
502 $a Thesis (Ph.D.) $c University of Minnesota $d 2017.
504 $a Includes bibliographical references
520 $a We use techniques from statistical mechanics to give evidence for new formulas for nonarchimedean metaplectic Whittaker functions, arising in the local theory of automorphic forms. We study a particular variation/generalization of the six-vertex model of type C having domain-wall boundary conditions dependent on a given integer partition lambda of length at most r, where r is a fixed positive integer. More precisely, we examine a planar, non-nested, U-turn model whose partition function Z lambda is related to characters of the symplectic group Sp(2 r, C).
520 $a We relate certain admissible states of our statistical-mechanical model to metaplectic Eisenstein series (or equivalently metaplectic Whittaker functions). We give a solution to the Yang--Baxter equation for metaplectic Boltzmann weights, which we use to derive two functional equations involving Zlambda, where one equation describes the action on Zlambda by a short simple root, while the other describes the action by a long simple root. Finally, we give evidence for the conjecture that Zlambda is a spherical Whittaker function by showing that Zlambda satisfies the same identities under our solution to the Yang--Baxter equation as the metaplectic Whittaker function under intertwining operators on the unramified principal series of an n-fold metaplectic cover of SO(2r + 1), for n odd.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Minnesota. $b Mathematics. $3 1180493
773 0 $t Dissertation Abstracts International $g 79-02B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10287518 $z click for full text (PQDT)

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