Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword immanant

 Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2010 (vol 63 pp. 413)

Konvalinka, Matjaž; Skandera, Mark
 Generating Functions for Hecke Algebra Characters Certain polynomials in $n^2$ variables that serve as generating functions for symmetric group characters are sometimes called ($S_n$) character immanants. We point out a close connection between the identities of Littlewood--Merris--Watkins and Goulden--Jackson, which relate $S_n$ character immanants to the determinant, the permanent and MacMahon's Master Theorem. From these results we obtain a generalization of Muir's identity. Working with the quantum polynomial ring and the Hecke algebra $H_n(q)$, we define quantum immanants that are generating functions for Hecke algebra characters. We then prove quantum analogs of the Littlewood--Merris--Watkins identities and selected Goulden--Jackson identities that relate $H_n(q)$ character immanants to the quantum determinant, quantum permanent, and quantum Master Theorem of Garoufalidis--L\^e--Zeilberger. We also obtain a generalization of Zhang's quantization of Muir's identity. Keywords:determinant, permanent, immanant, Hecke algebra character, quantum polynomial ringCategories:15A15, 20C08, 81R50
 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2015 : https://cms.math.ca/