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Weyl-Kac Character Formula for Affin...

Pakharev, Aleksei.

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Weyl-Kac Character Formula for Affine Lie Algebras in Deligne's Categories.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Weyl-Kac Character Formula for Affine Lie Algebras in Deligne's Categories./
Author:	Pakharev, Aleksei.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	49 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-11, Section: B.
Contained By:	Dissertations Abstracts International82-11B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28495725
ISBN:	9798728252085

Weyl-Kac Character Formula for Affine Lie Algebras in Deligne's Categories.
Pakharev, Aleksei.

Weyl-Kac Character Formula for Affine Lie Algebras in Deligne's Categories. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 49 p.

Source: Dissertations Abstracts International, Volume: 82-11, Section: B.

Thesis (Ph.D.)--Northeastern University, 2021.

This item must not be sold to any third party vendors.

We study the characters of simple modules in the parabolic BGG category of the affine Lie algebra in Deligne's category. More specifically, we take the limit of the Weyl-Kac formula to compute the character of the irreducible quotient of the parabolic Verma module with the dominant highest weight in a Deligne's category with t transcendental, and the base field of characteristic 0. We compare our result to the partial result in Etingof's paper, and evaluate the characters to the categorical dimensions to get a categorical interpretation of the Nekrasov-Okounkov hook length formula.

ISBN: 9798728252085Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Affile Lie algebra

Weyl-Kac Character Formula for Affine Lie Algebras in Deligne's Categories.
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245 1 0 $a Weyl-Kac Character Formula for Affine Lie Algebras in Deligne's Categories.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 49 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-11, Section: B.
500 $a Advisor: Toledano Laredo, Valerio;Etingof, Pavel.
502 $a Thesis (Ph.D.)--Northeastern University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a We study the characters of simple modules in the parabolic BGG category of the affine Lie algebra in Deligne's category. More specifically, we take the limit of the Weyl-Kac formula to compute the character of the irreducible quotient of the parabolic Verma module with the dominant highest weight in a Deligne's category with t transcendental, and the base field of characteristic 0. We compare our result to the partial result in Etingof's paper, and evaluate the characters to the categorical dimensions to get a categorical interpretation of the Nekrasov-Okounkov hook length formula.
590 $a School code: 0160.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Affile Lie algebra
653 $a Deligne's category
653 $a Nekrasov-Okounkov formula
653 $a Weyl-Kac character formula
653 $a Simple modules
653 $a Hook length
690 $a 0405
690 $a 0642
710 2 $a Northeastern University. $b Mathematics. $3 2098597
773 0 $t Dissertations Abstracts International $g 82-11B.
790 $a 0160
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28495725