RSK bases and Kazhdan-Lusztig cells
K. N. Raghavan, Preena Samuel, K. V. Subrahmanyam
TL;DR
This paper constructs RSK bases for quotients related to Kazhdan-Lusztig cells in symmetric groups, with applications to invariant theory and representation theory of the general linear group.
Contribution
It introduces RSK bases for specific quotients of group rings and Hecke algebras, linking combinatorial characterizations to algebraic structures.
Findings
RSK bases are constructed for certain quotients.
Applications to invariant theory over various base rings.
Insights into the representation theory of the symmetric group.
Abstract
From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, 'RSK bases' are constructed for certain quotients by two-sided ideals of the group ring and the Hecke algebra. Applications to invariant theory, over various base rings, of the general linear group and representation theory of the symmetric group are discussed.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics