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- Title
Representation theory of symmetric groups and the strong Lefschetz property.
- Authors
Kang, Seok-Jin; Kim, Young Rock; Shin, Yong-Su
- Abstract
We investigate the structure and properties of an Artinian monomial complete intersection quotient A (n , d) = [ x 1 , ... , x n ] / (x 1 d , ... , x n d). We construct explicit homogeneous bases of A (n , d) that are compatible with the S n -module structure for n = 3 , all exponents d ≥ 3 and all homogeneous degrees j ≥ 0. Moreover, we derive the multiplicity formulas, both in recursive form and in closed form, for each irreducible component appearing in the S 3 -module decomposition of homogeneous subspaces.
- Subjects
REPRESENTATIONS of groups (Algebra); REPRESENTATION theory; EXPONENTS; ARTIN rings; MULTIPLICITY (Mathematics)
- Publication
Journal of Algebra & Its Applications, 2022, Vol 21, Issue 3, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498822500554