東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Grothendieck resolution, affine Gras...

Shapiro, Alexander.

Linked to FindBook

Google Book

Amazon

博客來

Grothendieck resolution, affine Grassmannian, and Yangian.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Grothendieck resolution, affine Grassmannian, and Yangian./
Author:	Shapiro, Alexander.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
Description:	72 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.
Contained By:	Dissertation Abstracts International78-03B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10150877
ISBN:	9781369056426

Grothendieck resolution, affine Grassmannian, and Yangian.
Shapiro, Alexander.

Grothendieck resolution, affine Grassmannian, and Yangian. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 72 p.

Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.

Thesis (Ph.D.)--University of California, Berkeley, 2016.

In this thesis we address several questions on the structure and representation theory of quantum groups. The inspiration for problems and obtained solutions come from Poisson geometry. In the first chapter we classify the symplectic leaves on (a Poisson ind-subvariety of) the thick affine Grassmannian. Our classification extends previous results on the Poisson geometry of SLn-monopoles and the thin affine Grassmannian in type A. In the second chapter we show that a generic symplectic leaf (of maximal dimension) allows for a natural atlas and study transition maps between the charts. In particular we obtain a family of intertwining operators for the Yangian Y(gln) by quantizing these transition maps. Finally, the third chapter is devoted to a different but closely related problem. Namely, we construct a quantum version of the multiplicative Grothendieck-Springer resolution. As a corollary we obtain an embedding of the quantum group into the algebra of "quantum differential operators" on the principal affine space, realized as the Heisenberg double of the quantum Borel subalgebra.

ISBN: 9781369056426Subjects--Topical Terms:

515831
Mathematics.

Grothendieck resolution, affine Grassmannian, and Yangian.
LDR:01983nmm a2200277 4500 001 2122441
005 20170922124916.5
008 180830s2016 ||||||||||||||||| ||eng d
020 $a 9781369056426
035 $a (MiAaPQ)AAI10150877
035 $a AAI10150877
040 $a MiAaPQ $c MiAaPQ
100 1 $a Shapiro, Alexander. $3 646548
245 1 0 $a Grothendieck resolution, affine Grassmannian, and Yangian.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2016
300 $a 72 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.
500 $a Adviser: Nicolai Reshetikhin.
502 $a Thesis (Ph.D.)--University of California, Berkeley, 2016.
520 $a In this thesis we address several questions on the structure and representation theory of quantum groups. The inspiration for problems and obtained solutions come from Poisson geometry. In the first chapter we classify the symplectic leaves on (a Poisson ind-subvariety of) the thick affine Grassmannian. Our classification extends previous results on the Poisson geometry of SLn-monopoles and the thin affine Grassmannian in type A. In the second chapter we show that a generic symplectic leaf (of maximal dimension) allows for a natural atlas and study transition maps between the charts. In particular we obtain a family of intertwining operators for the Yangian Y(gln) by quantizing these transition maps. Finally, the third chapter is devoted to a different but closely related problem. Namely, we construct a quantum version of the multiplicative Grothendieck-Springer resolution. As a corollary we obtain an embedding of the quantum group into the algebra of "quantum differential operators" on the principal affine space, realized as the Heisenberg double of the quantum Borel subalgebra.
590 $a School code: 0028.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 $a University of California, Berkeley. $b Mathematics. $3 1685396
773 0 $t Dissertation Abstracts International $g 78-03B(E).
790 $a 0028
791 $a Ph.D.
792 $a 2016
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10150877