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Title: Standard Bases for Tensor Products of Exterior Powers
Authors: Howe, R
Kim, S
Lee Soo Teck 
Issue Date: 1-Jan-2019
Publisher: Springer Nature
Citation: Howe, R, Kim, S, Lee Soo Teck (2019-01-01). Standard Bases for Tensor Products of Exterior Powers. Algebras and Representation Theory. ScholarBank@NUS Repository.
Abstract: © 2019, Springer Nature B.V. For n ≥ a ≥ b, the tensor product V= ∧ a(ℂ n ) ⊗ ∧ b(ℂ n ) has a natural filtration 0 = V m+ 1 ⊆ V m ⊆⋯ ⊆ V 2 ⊆ V 1 ⊆ 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 .
Source Title: Algebras and Representation Theory
ISSN: 1386-923X
DOI: 10.1007/s10468-019-09869-5
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