Chari, Vyjayanthi, Fourier, Ghislain and Sagaki, Daisuke (2014). Posets, tensor products and Schur positivity. Algebr. Number Theory, 8 (4). S. 933 - 962. BERKELEY: MATHEMATICAL SCIENCE PUBL. ISSN 1944-7833
Full text not available from this repository.Abstract
Let g be a complex finite-dimensional simple Lie algebra. Given a positive integer k and a dominant weight lambda, we define a preorder <= on the set P+ (lambda, k) of k-tuples of dominant weights which add up to lambda. Let similar to be the equivalence relation defined by the preorder and P+ (lambda, k)/similar to be the corresponding poset of equivalence classes. We show that if lambda is a multiple of a fundamental weight (and k is general) or if k = 2 (and lambda is general), then P+ (lambda, k)/similar to coincides with the set of S-k-orbits in P+ (lambda, k), where S-k acts on P+ (lambda, k) as the permutations of components. If g is of type A(n) and k = 2, we show that the S-2-orbit of the row shuffle defined by Fomin et al. (2005) is the unique maximal element in the poset. Given an element of P+ (lambda, k), consider the tensor product of the corresponding simple finite-dimensional g-modules. We show that (for general g, lambda, and k) the dimension of this tensor product increases along <=. We also show that in the case when lambda is a multiple of a fundamental minuscule weight (g and k are general) or if g is of type A(2) and k = 2 (lambda is general), there exists an inclusion of tensor products along with the partial order <= on P+ (lambda, k)/similar to. In particular, if g is of type A(n), this means that the difference of the characters is Schur positive.
Item Type: | Journal Article | ||||||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-449341 | ||||||||||||||||
DOI: | 10.2140/ant.2014.8.933 | ||||||||||||||||
Journal or Publication Title: | Algebr. Number Theory | ||||||||||||||||
Volume: | 8 | ||||||||||||||||
Number: | 4 | ||||||||||||||||
Page Range: | S. 933 - 962 | ||||||||||||||||
Date: | 2014 | ||||||||||||||||
Publisher: | MATHEMATICAL SCIENCE PUBL | ||||||||||||||||
Place of Publication: | BERKELEY | ||||||||||||||||
ISSN: | 1944-7833 | ||||||||||||||||
Language: | English | ||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||
Subjects: | no entry | ||||||||||||||||
Uncontrolled Keywords: |
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URI: | http://kups.ub.uni-koeln.de/id/eprint/44934 |
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