Schubert calculus, adjoint representation and moment polytopes
Date
Authors
Editor(s)
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Print ISSN
Electronic ISSN
Publisher
Volume
Issue
Pages
Language
Type
Journal Title
Journal ISSN
Volume Title
Series
Abstract
Let Hν denote the irreducible representation of the special unitary group SU(n) corresponding to Young diagram ν and let g = su(n) denote the Lie algebra of SU(n). One can show that Hν appears in the symmetric algebra S∗ g if and only if n divides the size of the Young diagram ν. Kostant’s problem asks what is the least number N such that Hν appear in SN g. The moment polytope of the adjoint representation is the polytope generated by the normalized weights ν˜ such that Hν appears in S∗ g and it helps to put lower bounds on number N in the Kostant’s problem. In this thesis, we compute the moment polytope of the adjoint representation of SU(n) for n ≤ 9 using the solutions of the classical spectral problem and so-called ν-representability problem.