Multi-grounded partitions and character formulas
| Autor: | Jehanne Dousse, ISAAC KONAN |
|---|---|
| Přispěvatelé: | Dousse, Jehanne, Combinatoire, théorie des nombres (CTN), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA]
[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] General Mathematics 17B37 17B65 17B67 05A17 05E10 11P81 [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO] [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] Mathematics - Quantum Algebra [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] FOS: Mathematics Quantum Algebra (math.QA) Mathematics - Combinatorics Combinatorics (math.CO) Representation Theory (math.RT) [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT] Mathematics - Representation Theory |
| Zdroj: | HAL |
| Popis: | We introduce a new generalisation of partitions, multi-grounded partitions, related to ground state paths indexed by dominant weights of Lie algebras. We use these to express characters of irreducible highest weight modules of Kac-Moody algebras of affine type as generating functions for multi-grounded partitions. This generalises the approach of our previous paper, where only irreducible highest weight modules with constant ground state paths were considered, to all ground state paths. As an application, we compute the characters of the level $1$ modules of the affine Lie algebras $A_{2n}^{(2)}(n\geq 2)$, $D_{n+1}^{(2)}(n\geq 2)$, $A_{2n-1}^{(1)}(n\geq 3)$, $B_{n}^{(1)}(n\geq 3)$, and $D_{n}^{(1)}(n\geq 4)$. 26 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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