A Short Derivation of the Möbius Function for the Bruhat Order
John R. Stembridge
University of Michigan Department of Mathematics Ann Arbor Michigan 48109-1043 USA Ann Arbor Michigan 48109-1043 USA
DOI: 10.1007/s10801-006-0027-2
Abstract
We give a short, self-contained derivation of the Möbius function for the Bruhat orderings of Coxeter groups and their parabolic quotients.
Pages: 141–148
Keywords: keywords Coxeter group; Bruhat order; Möbius function
Full Text: PDF
References
1. A. Bj\ddot orner and F. Brenti, Combinatorics of Coxeter Groups, Springer, New York, 2005.
2. A. Bj\ddot orner and M. Wachs, “Bruhat order of Coxeter groups and shellability,” Adv. in Math. 43 (1982) 87-100. Springer J Algebr Comb (2007) 25:141-148
3. N. Bourbaki, Groupes et Alg`ebres de Lie, Chp. IV-VI, Masson, Paris, 1981.
4. F. Brenti, S. Fomin, and A. Postnikov, “Mixed Bruhat operators and Yang-Baxter equations for Weyl groups,” Internat. Math. Res. Notices 1999, 419-441.
5. V.V. Deodhar, “Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative M\ddot obius function,” Invent. Math. 39 (1977) 187-198.
6. M.J. Dyer, “Hecke algebras and shellings of Bruhat intervals,” Compositio Math. 89 (1993) 91-115.
7. J.E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Univ. Press, Cambridge, 1990.
8. A. Lascoux, “Anneau de Grothendieck de la variété de drapeaux,” in “The Grothendieck Festschrift, vol. III”, pp. 1-34, Progr. Math. 88, Birkh\ddot auser, Boston, 1990.
9. D. Kazhdan and G. Lusztig, “Representations of Coxeter groups and Hecke algebras,” Invent. Math. 53 (1979) 165-184.
10. D.-N. Verma, “M\ddot obius inversion for the Bruhat ordering on a Weyl group,” Ann. Sci. École Norm. Sup. 4 (1971) 393-398.
2. A. Bj\ddot orner and M. Wachs, “Bruhat order of Coxeter groups and shellability,” Adv. in Math. 43 (1982) 87-100. Springer J Algebr Comb (2007) 25:141-148
3. N. Bourbaki, Groupes et Alg`ebres de Lie, Chp. IV-VI, Masson, Paris, 1981.
4. F. Brenti, S. Fomin, and A. Postnikov, “Mixed Bruhat operators and Yang-Baxter equations for Weyl groups,” Internat. Math. Res. Notices 1999, 419-441.
5. V.V. Deodhar, “Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative M\ddot obius function,” Invent. Math. 39 (1977) 187-198.
6. M.J. Dyer, “Hecke algebras and shellings of Bruhat intervals,” Compositio Math. 89 (1993) 91-115.
7. J.E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Univ. Press, Cambridge, 1990.
8. A. Lascoux, “Anneau de Grothendieck de la variété de drapeaux,” in “The Grothendieck Festschrift, vol. III”, pp. 1-34, Progr. Math. 88, Birkh\ddot auser, Boston, 1990.
9. D. Kazhdan and G. Lusztig, “Representations of Coxeter groups and Hecke algebras,” Invent. Math. 53 (1979) 165-184.
10. D.-N. Verma, “M\ddot obius inversion for the Bruhat ordering on a Weyl group,” Ann. Sci. École Norm. Sup. 4 (1971) 393-398.