Relations between generalised Gelfand-Tsetlin and Kazhdan-Lusztig bases of $S_n$
Ali Haidar, Oded Yacobi
TL;DR
This paper establishes a triangular relationship between Kazhdan-Lusztig bases and generalized Gelfand-Tsetlin bases in Specht modules, revealing structural insights in representation theory of symmetric groups.
Contribution
It proves the upper triangularity of Kazhdan-Lusztig bases relative to all generalized Gelfand-Tsetlin bases derived from multiplicity-free towers.
Findings
Kazhdan-Lusztig basis is upper triangular w.r.t. generalized Gelfand-Tsetlin bases
Results hold for all bases constructed from multiplicity-free towers
Provides new structural understanding of Specht modules
Abstract
We prove that the Kazhdan-Lusztig basis of Specht modules is upper triangular with respect to all generalized Gelfand-Tsetlin bases constructed from any multiplicity-free tower of standard parabolic subgroups.
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Taxonomy
TopicsChemical Synthesis and Analysis · Coding theory and cryptography · Geometric and Algebraic Topology