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http://dx.doi.org/10.4134/CKMS.c190093

AN ARTINIAN RING HAVING THE STRONG LEFSCHETZ PROPERTY AND REPRESENTATION THEORY  

Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.2, 2020 , pp. 401-415 More about this Journal
Abstract
It is well-known that if char𝕜 = 0, then an Artinian monomial complete intersection quotient 𝕜[x1, …, xn]/(x1a1, …, xnan) has the strong Lefschetz property in the narrow sense, and it is decomposed by the direct sum of irreducible 𝖘𝖑2-modules. For an Artinian ring A = 𝕜[x1, x2, x3]/(x16, x26, x36), by the Schur-Weyl duality theorem, there exist 56 trivial representations, 70 standard representations, and 20 sign representations inside A. In this paper we find an explicit basis for A, which is compatible with the S3-module structure.
Keywords
The strong Lefschetz property; representation theory; Artinian monomial complete intersection quotients; Hilbert functions;
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