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The symplectic geometry of the Gel'f...

Harada, Megumi.

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The symplectic geometry of the Gel'fand-Cetlin-Molev basis for representations of Sp(2n, C ).

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The symplectic geometry of the Gel'fand-Cetlin-Molev basis for representations of Sp(2n, C )./
作者:	Harada, Megumi.
面頁冊數:	101 p.
附註:	Source: Dissertation Abstracts International, Volume: 64-09, Section: B, page: 4397.
Contained By:	Dissertation Abstracts International64-09B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3105234
ISBN:	0496528017

The symplectic geometry of the Gel'fand-Cetlin-Molev basis for representations of Sp(2n, C ).
Harada, Megumi.

The symplectic geometry of the Gel'fand-Cetlin-Molev basis for representations of Sp(2n, C ). - 101 p.

Source: Dissertation Abstracts International, Volume: 64-09, Section: B, page: 4397.

Thesis (Ph.D.)--University of California, Berkeley, 2003.

The Gel'fand-Cetlin canonical basis for a finite-dimensional representation V(lambda) of U(n, C ) can be constructed by successive decompositions of the representation by a chain of subgroups U1,C ⊂U 2,C ⊂&ldots;Un- 1,C ⊂U n, C. A key point in the construction is that the decomposition of an irreducible representation of U(k, C ) by the subgroup U(k - 1, C ) is multiplicity-free. Guillemin and Sternberg constructed in the 1980s the Gel'fand-Cetlin integrable system on the coadjoint orbits of U(n, C ), which is the symplectic geometric version of the Gel'fand-Cetlin basis. Much the same construction works for representations of O( n) = U(n, R ).

ISBN: 0496528017Subjects--Topical Terms:

515831
Mathematics.

The symplectic geometry of the Gel'fand-Cetlin-Molev basis for representations of Sp(2n, C ).
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245 1 4 $a The symplectic geometry of the Gel'fand-Cetlin-Molev basis for representations of Sp(2n, C ).
300 $a 101 p.
500 $a Source: Dissertation Abstracts International, Volume: 64-09, Section: B, page: 4397.
500 $a Chair: Allen Knutson.
502 $a Thesis (Ph.D.)--University of California, Berkeley, 2003.
520 $a The Gel'fand-Cetlin canonical basis for a finite-dimensional representation V(lambda) of U(n, C ) can be constructed by successive decompositions of the representation by a chain of subgroups U1,C ⊂U 2,C ⊂&ldots;Un- 1,C ⊂U n, C. A key point in the construction is that the decomposition of an irreducible representation of U(k, C ) by the subgroup U(k - 1, C ) is multiplicity-free. Guillemin and Sternberg constructed in the 1980s the Gel'fand-Cetlin integrable system on the coadjoint orbits of U(n, C ), which is the symplectic geometric version of the Gel'fand-Cetlin basis. Much the same construction works for representations of O( n) = U(n, R ).
520 $a For G = U(n, H ), the compact symplectic group, the decompositions are not multiplicity-free. However, Molev recently found a Gel'fand-Cetlin type basis for representations of the symplectic group, using essentially new ideas. An important new role is played by the Yangian Y(2), an infinite-dimensional Hopf algebra, and a subalgebra of Y(2) called the twisted Yangian Y-(2). In this thesis I use deformation theory to find the symplectic and Poisson geometric analogue of Molev's result, thus constructing a new integrable system on the coadjoint orbits of U(n, H ).
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