Weak order on complete quadrics
HTML articles powered by AMS MathViewer
- by Mahir Bilen Can and Michael Joyce PDF
- Trans. Amer. Math. Soc. 365 (2013), 6269-6282 Request permission
Abstract:
Using an action of the Richardson-Springer monoid on involutions, we study the weak order on the variety of complete quadrics. Maximal chains in the poset are explicitly determined. Applying results of Brion, our calculations describe certain cohomology classes in the complete flag variety.References
- Eli Bagno and Yonah Cherniavsky, Congruence $B$-orbits and the Bruhat poset of involutions of the symmetric group, Discrete Math. 312 (2012), no. 6, 1289–1299. MR 2876381, DOI 10.1016/j.disc.2011.12.018
- Michel Brion, The behaviour at infinity of the Bruhat decomposition, Comment. Math. Helv. 73 (1998), no. 1, 137–174. MR 1610599, DOI 10.1007/s000140050049
- Michel Brion, On orbit closures of spherical subgroups in flag varieties, Comment. Math. Helv. 76 (2001), no. 2, 263–299. MR 1839347, DOI 10.1007/PL00000379
- M.B. Can and M. Joyce, Ordered Bell numbers, Hermite polynomials, skew Young tableaux, and Borel orbits, Submitted for publication.
- M.B. Can and L.E. Renner, Bruhat-Chevalley order on the rook monoid, Turkish J. Math. 35 (2011), no. 2, 1–21.
- C. De Concini and C. Procesi, Complete symmetric varieties, Invariant theory (Montecatini, 1982) Lecture Notes in Math., vol. 996, Springer, Berlin, 1983, pp. 1–44. MR 718125, DOI 10.1007/BFb0063234
- Charles Ehresmann, Sur la topologie de certains espaces homogènes, Ann. of Math. (2) 35 (1934), no. 2, 396–443 (French). MR 1503170, DOI 10.2307/1968440
- Federico Incitti, The Bruhat order on the involutions of the symmetric group, J. Algebraic Combin. 20 (2004), no. 3, 243–261. MR 2106960, DOI 10.1023/B:JACO.0000048514.62391.f4
- Friedrich Knop, On the set of orbits for a Borel subgroup, Comment. Math. Helv. 70 (1995), no. 2, 285–309. MR 1324631, DOI 10.1007/BF02566009
- Edwin A. Pennell, Mohan S. Putcha, and Lex E. Renner, Analogue of the Bruhat-Chevalley order for reductive monoids, J. Algebra 196 (1997), no. 2, 339–368. MR 1475115, DOI 10.1006/jabr.1997.7111
- Mohan S. Putcha, Shellability in reductive monoids, Trans. Amer. Math. Soc. 354 (2002), no. 1, 413–426. MR 1859281, DOI 10.1090/S0002-9947-01-02806-9
- Mohan S. Putcha, Bruhat-Chevalley order in reductive monoids, J. Algebraic Combin. 20 (2004), no. 1, 34–53. MR 2104819, DOI 10.1023/B:JACO.0000047291.42015.a6
- Lex E. Renner, Analogue of the Bruhat decomposition for algebraic monoids, J. Algebra 101 (1986), no. 2, 303–338. MR 847163, DOI 10.1016/0021-8693(86)90197-3
- Lex E. Renner, Linear algebraic monoids, Encyclopaedia of Mathematical Sciences, vol. 134, Springer-Verlag, Berlin, 2005. Invariant Theory and Algebraic Transformation Groups, V. MR 2134980
- R. W. Richardson and T. A. Springer, The Bruhat order on symmetric varieties, Geom. Dedicata 35 (1990), no. 1-3, 389–436. MR 1066573, DOI 10.1007/BF00147354
- R. W. Richardson and T. A. Springer, Complements to: “The Bruhat order on symmetric varieties” [Geom. Dedicata 35 (1990), no. 1-3, 389–436; MR1066573 (92e:20032)], Geom. Dedicata 49 (1994), no. 2, 231–238. MR 1266276, DOI 10.1007/BF01610623
- T. A. Springer, Combinatorics of $B$-orbits in a wonderful compactification, Algebraic groups and arithmetic, Tata Inst. Fund. Res., Mumbai, 2004, pp. 99–117. MR 2094109
Additional Information
- Mahir Bilen Can
- Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70130
- Michael Joyce
- Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70130
- Received by editor(s): January 11, 2012
- Received by editor(s) in revised form: February 17, 2012
- Published electronically: July 10, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 6269-6282
- MSC (2010): Primary 14M17; Secondary 14L30
- DOI: https://doi.org/10.1090/S0002-9947-2013-05813-8
- MathSciNet review: 3105751