×

zbMATH — the first resource for mathematics

Equivalence classes for the \(\mu\)-coefficient of Kazhdan-Lusztig polynomials in \(S_n\). (English) Zbl 1263.05118
Summary: We study equivalence classes relating to the Kazhdan-Lusztig \(\mu(x,w)\) coefficients in order to help explain the scarcity of distinct values. Each class is conjectured to contain a “crosshatch” pair. We also compute the values attained by \(\mu(x,w)\) for the permutation groups \(S_10\) and \(S_11\).

MSC:
05E10 Combinatorial aspects of representation theory
20F55 Reflection and Coxeter groups (group-theoretic aspects)
PDF BibTeX XML Cite
Full Text: DOI Euclid arXiv
References:
[1] Beilinson [Beilinson and Bernstein 81] A., C. R. Acad. Sci. Paris Ser. I Math 292 pp 15– (1981)
[2] DOI: 10.1007/978-1-4612-1324-6 · doi:10.1007/978-1-4612-1324-6
[3] DOI: 10.1090/S0002-9947-03-03019-8 · Zbl 1037.14020 · doi:10.1090/S0002-9947-03-03019-8
[4] Björner [Björner and Brenti 05] Anders, Combinatorics of Coxeter Groups, Graduate Texts in Mathematics 231 (2005)
[5] DOI: 10.1090/S0894-0347-98-00249-5 · Zbl 0904.20033 · doi:10.1090/S0894-0347-98-00249-5
[6] DOI: 10.1016/j.ejc.2003.10.011 · Zbl 1064.14062 · doi:10.1016/j.ejc.2003.10.011
[7] DOI: 10.1016/j.jalgebra.2005.12.030 · Zbl 1113.20038 · doi:10.1016/j.jalgebra.2005.12.030
[8] DOI: 10.1016/j.aim.2005.01.011 · Zbl 1091.05075 · doi:10.1016/j.aim.2005.01.011
[9] DOI: 10.1007/BF01389272 · Zbl 0473.22009 · doi:10.1007/BF01389272
[10] du Cloux, [du Cloux 11] F. 2011. ”Coxeter3.” Available online (http://math.univ-lyon1.fr/ducloux/coxeter/coxeter3/english/coxeter3_e.html).
[11] Fulton [Fulton 97] William, Young Tableaux, London Mathematical Society Student Texts 35 (1997)
[12] DOI: 10.1090/S0002-9947-08-04478-4 · Zbl 1154.05002 · doi:10.1090/S0002-9947-08-04478-4
[13] Hanson, [Hanson 11] Troy D. 2011. ”Uthash: A Hash Table for C Structures.” Available online (http://uthash.sourceforge.net).
[14] Humphreys [Humphreys 90] James E., Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics 29 (1990) · Zbl 0725.20028 · doi:10.1017/CBO9780511623646
[15] Jenkins, [Jenkins 11] B. 2011. ”A Hash Function for Hash Table Lookup.” Available online (http://burtleburtle.net/bob/c/lookup3.c).
[16] DOI: 10.1007/BF01390031 · Zbl 0499.20035 · doi:10.1007/BF01390031
[17] Kazhdan [Kazhdan and Lusztig 80] D., Proc. Symp. Pure. Math., A.M.S. 36 pp 185– (1980) · doi:10.1090/pspum/036/573434
[18] Knuth [Knuth 70] Donald E., Pacific J. Math. 34 pp 709– (1970) · Zbl 0199.31901 · doi:10.2140/pjm.1970.34.709
[19] Knutson, [Knutson 70] Allen. 2009. Personal communication.
[20] DOI: 10.1090/S1088-4165-03-00178-X · Zbl 1014.05068 · doi:10.1090/S1088-4165-03-00178-X
[21] DOI: 10.1016/j.jalgebra.2007.08.018 · Zbl 1187.20003 · doi:10.1016/j.jalgebra.2007.08.018
[22] Warrington, [Warrington 11] Gregory S. 2011. ”klc.” Available online (http://www.cems.uvm.edu/gwarring/research/klc.html).
[23] DOI: 10.1016/j.jalgebra.2004.08.039 · Zbl 1068.20003 · doi:10.1016/j.jalgebra.2004.08.039
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.