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Graded multiplicities of the nullcone for the algebraic symmetric pair of type G [microform]
Bib ID 4398383
Format BookBook, MicroformMicroform, OnlineOnline
Author
Van Groningen, Anthony Paul
 
Online Versions
Description 108 p. 
ISBN 9780549014485
Summary

The regular functions on the nullcone associated to the algebraic symmetric pair (G2, so (4, C )) of Type G is decomposed as a graded representation of K = SO(4, C ). This is done in two complementary ways. First a formula for the graded multiplicities in terms of the principal branching rule for sp (2, C ) is derived using an application of Howe duality. Second, an explicit formula for the q-multiplicity of each K-type is given. As a consequence, a closed rational form for the Hilbert series of C [G2]K is determined. Branching from a simple Lie algebra to a principal three-dimensional subalgebra is discussed in the context of Kostant's multiplicity formula. The support of the relevant partition function is described in terms of the Bruhat order. Using the methods of Heckman, asymptotic estimates for the principal branching multiplicities of a simple Lie algebra, g are shown to be related to the exponents g .

The case of g = sp (2, C ) is studied in further detail and these calculations are used to describe the asymptotic distribution of the graded multiplicities in Type G. The symmetric pair (G2, so (4, C )) leads to the study of binary (3, 1)-forms for which a complete system of covariant generators is known. From this the Brion polytope for the nullcone is determined.

Notes

(UMI)AAI3262944

Source: Dissertation Abstracts International, Volume: 68-05, Section: B, page: 3098.

Advisers: Allen D. Bell; Jeb W. Willenbring.

Thesis (Ph.D.)--The University of Wisconsin - Milwaukee, 2007.

Reproduction Microfiche. Ann Arbor, Mich. : University Microfilms International. 
Subjects Mathematics.
Other authors/contributors The University of Wisconsin - Milwaukee

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