Murnaghan-Nakayama rules for characters

of Iwahori-Hecke algebras of classical type

Authors:
Tom Halverson and Arun Ram

Journal:
Trans. Amer. Math. Soc. **348** (1996), 3967-3995

MSC (1991):
Primary 20C05; Secondary 05E05

DOI:
https://doi.org/10.1090/S0002-9947-96-01491-2

MathSciNet review:
1322951

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we give Murnaghan-Nakayama type formulas for computing the irreducible characters of the Iwahori-Hecke algebras of types , and . Our method is a generalization of a derivation of the Murnaghan-Nakayama formula for the irreducible characters of the symmetric group given by Curtis Greene. Greene's approach is to sum up the diagonal entries of the matrices of certain cycle permutations in Young's seminormal representations. The analogues of the Young seminormal representations for the Iwahori-Hecke algebras of types , and were given by Hoefsmit.

**[AK]**S. Ariki and K. Koike,*A Hecke algebra of and construction of its irreducible representations*, Adv. in Math.**106**(1994), 216--243. MR**95h:20006****[ATY]**S. Ariki, T. Terasoma, and H. Yamada,*Schur-Weyl reciprocity for the Hecke algebra of*, preprint 1994.**[CK1]**C. J. Cummins and R. C. King,*Frobenius formula for characters of Hecke algebras of type*, Comm. Algebra**21**(12) (1993), 4397--4423. MR**95b:20011****[CK2]**------,*An algorithm for calculating characters of Hecke algebras of type when is a root of unity*, Comm. Algebra**21**(12) (1993), 4425--4437. MR**95b:20012****[Ge]**M. Geck,*On the character values of Iwahori-Hecke algebras of exceptional type*, Proc. London Math. Soc. (3)**68**(1994), 51--76. MR**94i:20073****[GP]**M. Geck and G. Pfeiffer,*On the irreducible characters of Hecke algebras*, Adv. in Math.**102**(1993), 79--94. MR**94m:20018****[Gr]**C. Greene,*A rational function identity related to the Murnaghan-Nakayama formula for the characters of*, J. Alg. Comb.**1**(1992), 235--255. MR**93k:20025****[H]**P. N. Hoefsmit,*Representations of Hecke algebras of finite groups with -pairs of classical type*, Thesis, Univ. of British Columbia, 1974.**[KW]**R. C. King and B. G. Wybourne,*Representations and traces of the Hecke algebras of type*, J. Math. Phys.**33**(1992), 4--14. MR**93c:20028****[LR]**R. Leduc and A. Ram,*A ribbon Hopf algebra approach to the irreducible representations of centralizer algebras*, The Brauer, Birman-Wenzl, and Type A Iwahori-Hecke algebras, Adv. in Math. (to appear).**[Mac]**I. G. Macdonald,*Symmetric functions and Hall polynomials*, Oxford Univ. Press, 1979. MR**84g:05003****[P]**G. Pfeiffer,*Young characters on Coxeter basis elements of Iwahori-Hecke algebras and a Murnaghan-Nakayama formula*, J. Algebra**168**(1994), 525--535. MR**95g:20012****[R]**A. Ram,*A Frobenius formula for the characters of the Hecke algebras*, Invent. Math.**106**(1991), 461--488. MR**93c:20029****[Sta]**R. Stanley,*Enumerative combinatorics*, vol. I, Wadsworth & Brooks/Cole, 1986. MR**87j:05003****[Ste]**J. Stembridge, unpublished notes, 1987.**[vdJ]**J. van der Jeugt,*An algorithm for characters of Hecke algebras of type*, J. Phys. A**24**(1991), 3719--3724. MR**91i:05224****[Y]**A. Young,*Quantitative substitutional analysis*I--IX, Proc. London Math. Soc. (1901--1952). MR**14:126e**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (1991):
20C05,
05E05

Retrieve articles in all journals with MSC (1991): 20C05, 05E05

Additional Information

**Tom Halverson**

Affiliation:
Department of Mathematics, Macalester College, St. Paul, Minnesota 55105

Email:
halverson@macalstr.edu

**Arun Ram**

Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Address at time of publication:
Department of Mathematics, Princeton University, Princeton, New Jersey 08544

DOI:
https://doi.org/10.1090/S0002-9947-96-01491-2

Received by editor(s):
October 20, 1994

Additional Notes:
Supported in part by a National Science Foundation postdoctoral fellowship DMS-9107863

Article copyright:
© Copyright 1996
American Mathematical Society