A new approach to a theorem of Eng
The main aim of this work is to give a case-free algebraic proof for a theorem of Eng on the Poincaré polynomial of parabolic quotients of finite Coxeter groups evaluated at -1.
Keywords:
Coxeter groups, descent algebras, Poincaré polynomial, the longest element $q=-1$ phenomenon,
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- [1] D. Blessenohl, C. Hohlweg and M. Schocker, A symmetry of the descent algebra of a finite Coxeter group, Adv. Math. 193 (2), 416-437, 2005.
- [2] C.W. Curtis and I. Reiner, Methods of Representation Theory with Applications to Finite Groups and Orders Vol. II, John Wiley and Sons, 1987.
- [3] O. Eng, Quotients of Poincaré polynomials evaluated at -1, J. Algebraic Combin. 13 (1), 29-40, 2001.
- [4] J.E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Studies in Ad- vanced Mathematics 29, Cambridge University Press, 1990.
- [5] V. Reiner, Note on a theorem of Eng, Ann. Comb. 6 (1), 117-118, 2002.
- [6] V. Reiner, D. Stanton and D. White, The cyclic sieving phenomenon, J. Combin. Theory Ser. A 108 (1), 17-50, 2004.
- [7] L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra 41 (2), 255-264, 1976.
- Yayın Aralığı: Yılda 6 Sayı
- Başlangıç: 2002
- Yayıncı: Hacettepe Üniversitesi Fen Fakultesi
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