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Symplectic approaches in geometric r...

Jin, Xin.

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Symplectic approaches in geometric representation theory.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Symplectic approaches in geometric representation theory./
作者:	Jin, Xin.
面頁冊數:	95 p.
附註:	Source: Dissertation Abstracts International, Volume: 77-01(E), Section: B.
Contained By:	Dissertation Abstracts International77-01B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3720585
ISBN:	9781339016207

Symplectic approaches in geometric representation theory.
Jin, Xin.

Symplectic approaches in geometric representation theory. - 95 p.

Source: Dissertation Abstracts International, Volume: 77-01(E), Section: B.

Thesis (Ph.D.)--University of California, Berkeley, 2015.

We study various topics lying in the crossroads of symplectic topology and geometric representation theory, with an emphasis on understanding central objects in geometric representation theory via approaches using Lagrangian branes and symplectomorphism groups.

ISBN: 9781339016207Subjects--Topical Terms:

515831
Mathematics.

Symplectic approaches in geometric representation theory.
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500 $a Source: Dissertation Abstracts International, Volume: 77-01(E), Section: B.
500 $a Adviser: David Nadler.
502 $a Thesis (Ph.D.)--University of California, Berkeley, 2015.
520 $a We study various topics lying in the crossroads of symplectic topology and geometric representation theory, with an emphasis on understanding central objects in geometric representation theory via approaches using Lagrangian branes and symplectomorphism groups.
520 $a The first part of the dissertation focuses on a natural link between perverse sheaves and holomorphic Lagrangian branes. For a compact complex manifold X, let Dcb(X) be the bounded derived category of constructible sheaves on X, and Fuk(T*X) be the Fukaya category of T*X. A Lagrangian brane in Fuk(T*X) is holomorphic if the underlying Lagrangian submanifold is complex analytic in T*XC , the holomorphic cotangent bundle of X. We prove that under the quasi-equivalence between Dcb(X) and DFuk(T*X) established by Nadler and Zaslow, holomorphic Lagrangian branes with appropriate grading correspond to perverse sheaves.
520 $a The second part is motivated from general features of the braid group actions on derived category of constructible sheaves. For a semisimple Lie group GC over C, we study the homotopy type of the symplectomorphism group of the cotangent bundle of the flag variety and its relation to the braid group. We prove a homotopy equivalence between the two groups in the case of GC = SL 3(C), under the SU(3)-equivariancy condition on symplectomorphisms.
590 $a School code: 0028.
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710 2 $a University of California, Berkeley. $b Mathematics. $3 1685396
773 0 $t Dissertation Abstracts International $g 77-01B(E).
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