Kostant $ρ$-decomposition of homology I. Finite-dimensional representations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911188603895808 |
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| author | Sam, Steven V VandeBogert, Keller Weyman, Jerzy |
| author_facet | Sam, Steven V VandeBogert, Keller Weyman, Jerzy |
| contents | We give explicit, uniform formulas for the graded characters and total ranks of the Lie algebra homology of finite-dimensional representations in all classical types. In many cases, these compute the Tor groups of finite length modules over polynomial rings, and this is the first in a series of papers to investigate total rank conjectures from this perspective. These formulas refine and generalize the classical $ρ$-decomposition of Kostant, and in particular we prove that the characters involved exhibit three structural phenomena: divisibility (by a large power of 2), equidistribution, and uniform factorization formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kostant $ρ$-decomposition of homology I. Finite-dimensional representations Sam, Steven V VandeBogert, Keller Weyman, Jerzy Representation Theory Commutative Algebra Combinatorics We give explicit, uniform formulas for the graded characters and total ranks of the Lie algebra homology of finite-dimensional representations in all classical types. In many cases, these compute the Tor groups of finite length modules over polynomial rings, and this is the first in a series of papers to investigate total rank conjectures from this perspective. These formulas refine and generalize the classical $ρ$-decomposition of Kostant, and in particular we prove that the characters involved exhibit three structural phenomena: divisibility (by a large power of 2), equidistribution, and uniform factorization formulas. |
| title | Kostant $ρ$-decomposition of homology I. Finite-dimensional representations |
| topic | Representation Theory Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2510.01343 |