Mark Skandera ; Justin Lambright - An immanant formulation of the dual canonical basis of the quantum polynomial ring

dmtcs:2703 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2703
An immanant formulation of the dual canonical basis of the quantum polynomial ringArticle

Authors: Mark Skandera 1; Justin Lambright 1

  • 1 Department of Mathematics [Bethlehem, USA]

We show that dual canonical basis elements of the quantum polynomial ring in $n^2$ variables can be expressed as specializations of dual canonical basis elements of $0$-weight spaces of other quantum polynomial rings. Our results rely upon the natural appearance in the quantum polynomial ring of Kazhdan-Lusztig polynomials, $R$-polynomials, and certain single and double parabolic generalizations of these.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: Dual canonical basis,immanant,Kazhdan-Lusztig polynomial,Hecke algebra,quantum polynomial ring,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

1 Document citing this article

Consultation statistics

This page has been seen 149 times.
This article's PDF has been downloaded 149 times.