Unique factorization of tensor products for Kac-Moody Algebras
Material type:
TextPublication details: 2013Description: 38pSubject(s): Mathematics | HBNI Th55 | Kac-Moody Algebras | Tensor ProductsOnline resources: Click here to access online Dissertation note: 2013Ph.DHBNI Abstract: In the first part, we address a fundamental question, unique factorization of tensor products, that arises in representation theory. We consider integrable, category O modules of indecomposable symmetrizable Kac-Moody algebras. We prove that unique factorization of tensor products of irreducible modules holds in this category, upto twisting by one dimensional modules. This generalizes a fundamental theorem of Rajan for finite dimensional simple Lie algebras over C. Our proof is new even for the finite dimensional case, and uses an interplay of representation theory and combinatorics to analyze the Kac-Weyl character formula. In the second part, we get a new interpretation of the chromatic polynomials using Kac-Moody theory and derive some of its properties using this new interpretation.
THESIS & DISSERTATION
| Current library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
| IMSc Library | IMSc Library | HBNI Th55 (Browse shelf (Opens below)) | Link to resource | Available | 68695 |
2013
Ph.D
HBNI
In the first part, we address a fundamental question, unique factorization of tensor products, that arises in representation theory. We consider integrable, category O modules of indecomposable symmetrizable Kac-Moody algebras. We prove that unique factorization of tensor products of irreducible modules holds in this category, upto twisting by one dimensional modules. This generalizes a fundamental theorem of Rajan for finite dimensional simple Lie algebras over C. Our proof is new even for the finite dimensional case, and uses an interplay of representation theory and combinatorics to analyze the Kac-Weyl character formula. In the second part, we get a new interpretation of the chromatic polynomials using Kac-Moody theory and derive some of its properties using this new interpretation.
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