Standard Bases for Tensor Products of Exterior Powers
- Authors
- Howe, Roger; Kim, Sangjib; Lee, Soo Teck
- Issue Date
- 6월-2020
- Publisher
- SPRINGER
- Keywords
- General linear group; Tensor product; Exterior powers; Standard basis
- Citation
- ALGEBRAS AND REPRESENTATION THEORY, v.23, no.3, pp.715 - 738
- Indexed
- SCIE
SCOPUS
- Journal Title
- ALGEBRAS AND REPRESENTATION THEORY
- Volume
- 23
- Number
- 3
- Start Page
- 715
- End Page
- 738
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/55504
- DOI
- 10.1007/s10468-019-09869-5
- ISSN
- 1386-923X
- Abstract
- For n >= a >= b, the tensor product V = Lambda(a)(C-n) circle times Lambda(b)(C-n)has a natural filtration 0 = Vm+ 1 subset of V-m subset of ... subset of V-2 subset of V-1 subset of V-0 = V of Gl(n) submodules where m = min(n - a,b) and V/V-1 is the Cartan product. For each 1 <= u <= m, we construct a basis for V-u and a basis for the quotient V/V-u. The elements in the basis for V-u can be regarded as a generalization of the quadratic relations, and the elements in the basis for V/V-u are parametrized by a set of skew tableaux satisfying a condition that cleanly extends the well known semistandardness condition defining a basis for V/V-1.
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