자료유형  

 학위논문

Control Number  

0016932560

International Standard Book Number  

9798379680749

Dewey Decimal Classification Number  

512

Main Entry-Personal Name  

Huang, Chenliang.

Publication, Distribution, etc. (Imprint  

[S.l.] : Purdue University., 2020

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2020

Physical Description  

1 online resource(135 p.)

General Note  

Source: Dissertations Abstracts International, Volume: 84-12, Section: B.

General Note  

Advisor: Mukhin, Evgeny.

Dissertation Note  

Thesis (Ph.D.)--Purdue University, 2020.

Restrictions on Access Note  

This item must not be sold to any third party vendors.

Summary, Etc.  

요약We describe a reproduction procedure which, given a solution of the glm|n Gaudin Bethe ansatz equation associated to a tensor product of polynomial modules, produces a family P of other solutions called the population. To a population we associate a rational pseudodifferential operator R and a superspace W of rational functions.We show that if at least one module is typical then the population P is canonically identified with the set of minimal factorizations of R and with the space of full superflags in W. We conjecture that the singular eigenvectors (up to rescaling) of all glm|n Gaudin Hamiltonians are in a bijective correspondence with certain superspaces of rational functions.We establish a duality of the non-periodic Gaudin model associated with superalgebra glm|n and the non-periodic Gaudin model associated with algebra glk . The Hamiltonians of the Gaudin models are given by expansions of a Berezinian of an (m + n) x (m + n) matrix in the case of glm|n and of a column determinant of a k x k matrix in the case of glk . We obtain our results by proving Capelli type identities for both cases and comparing the results.We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian Y(glm|n ). To a solution we associate a rational difference operator D and a superspace of rational functions W. We show that the set of complete factorizations of D is in canonical bijection with the variety of superflags in W and that each generic superflag defines a solution of the Bethe ansatz equation. We also give the analogous statements for the quasi-periodic supersymmetric spin chains.

Subject Added Entry-Topical Term  

Eigenvalues.

Subject Added Entry-Topical Term  

Algebra.

Subject Added Entry-Topical Term  

Polynomials.

Subject Added Entry-Topical Term  

Eigenvectors.

Subject Added Entry-Topical Term  

Mathematics.

Added Entry-Corporate Name  

Purdue University.

Host Item Entry  

Dissertations Abstracts International. 84-12B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

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Control Number  

joongbu:641383