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Mathematics > Quantum Algebra

Title: Multiplication formulas and semisimplicity for q-Schur superalgebras

Abstract: We investigate products of certain double cosets for the symmetric group and use the findings to derive some multiplication formulas for q-Schur superalgebras. This gives a combinatorialisation of the relative norm approach developed by the first two authors. We then give several applications of the multiplication formulas, including the matrix representation of the regular representation and a semisimplicity criterion for q-Schur superalgebras. We also construct infinitesimal and little q-Schur superalgebras directly from the multiplication formulas and develop their semisimplicity criteria.
Comments: 22 pages. Nagoya J. Math. (to appear)
Subjects: Quantum Algebra (math.QA); Group Theory (math.GR); Rings and Algebras (math.RA); Representation Theory (math.RT)
Cite as: arXiv:1803.06463 [math.QA]
  (or arXiv:1803.06463v1 [math.QA] for this version)

Submission history

From: Jie Du [view email]
[v1] Sat, 17 Mar 2018 04:59:39 GMT (24kb)