National Library of Australia

Preview the redeveloped Catalogue before it launches late July.

Due to major building activity, some collections are unavailable. Please check your requests before visiting. Learn more.

You must be logged in to Tag Records
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

In the Library

Request this item to view in the Library's reading rooms using your library card. To learn more about how to request items watch this short online video Help Video.

Details Collect From
mc 252 32-62944 Main Reading Room - Newspapers and Family History

Order a copy

- Copyright or permission restrictions may apply. We will contact you if necessary.

Help Video To learn more about Copies Direct watch this short online video Help Video.
close Can I borrow items from the Library?

You need Flash player 8+ and JavaScript enabled to view this video embedded.

You can view this on the NLA website.

close What can I get online?

You need Flash player 8+ and JavaScript enabled to view this video embedded.

You can view this on the NLA website.

close Can I get copies of items from the Library?

You need Flash player 8+ and JavaScript enabled to view this video embedded.

You can view this on the NLA website.

Aboriginal and Torres Strait Islander Flags
Aboriginal, Torres Strait Islander and other First Nations people are advised that this catalogue contains names, recordings and images of deceased people and other content that may be culturally sensitive. Please also be aware that you may see certain words or descriptions in this catalogue which reflect the author’s attitude or that of the period in which the item was created and may now be considered offensive.