Algebra and geometry of Gelfand-Tsetlin patterns
The problem of studying special bases in irreducible representations of Lie groups has already attracted a lot of attention. Algebraic and geometric structures arising from these bases are of great importance due to numerous applications in various areas of modern mathematics and physics. This t...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2020
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| Online Access: | https://eprints.nottingham.ac.uk/60557/ |
| Summary: | The problem of studying special bases in irreducible representations of Lie groups has already attracted a lot of attention. Algebraic and geometric structures arising from these bases are of great importance due to numerous applications in various areas of modern mathematics and physics.
This thesis is devoted to detailed study of Gelfand-Tsetlin patterns appearing in explicit formulas for certain special functions on classical groups. Originally Gelfand-Tsetlin patterns appeared in parametrization of basis of finite-dimensional representations. Remarkably the same patterns (in the form of Givental-GLO graphs) appear in integral representations of Whittaker functions related to principal series (infinite-dimensional) representations of Lie groups. We study basic properties of Gelfand-Tsetlin patterns appearing both for finite-dimensional and infinite-dimensional representations and uncover relations between them. |
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