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Kazhdan–Lusztig immanants and products of matrix minors, II
- DOI:
- 10.1080/03081080701646638
pages 137-150
Available online: 20 Jan 2009Abstract
We show that for each permutation w containing no decreasing subsequence of length k, the Kazhdan–Lusztig immanant Imm w (x) vanishes on all matrices having k equal rows or columns. Also, we define two filtrations of the vector space of immanants via products of matrix minors and pattern avoidance and use the above result to show that these filtrations are equivalent. Finally, we construct new and simple inequalities satisfied by the minors of totally nonnegative matrices.
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- Available online: 20 Jan 2009
Author affiliations
- a Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
- b Department of Mathematics, Lehigh University, Bethlehem, PA 18015, USA
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