Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165

 
 

 

Closures of $ K$-orbits in the flag variety for $ SU^*(2n)$


Author: William M. McGovern
Journal: Represent. Theory 15 (2011), 568-573
MSC (2010): Primary 22E47, 57S25
DOI: https://doi.org/10.1090/S1088-4165-2011-00386-1
Published electronically: July 12, 2011
MathSciNet review: 2833467
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize the $ Sp_{2n}$-orbits in the flag variety for $ SL_{2n}$ with rationally smooth closure via a pattern avoidance criterion, also showing that the singular and rationally singular loci of such orbit closures coincide.


References [Enhancements On Off] (What's this?)

  • [B98] S. Billey, Pattern avoidance and rational smoothness for Schubert varieties, Adv. in Math. 139 (1998), 141-156. MR 1652522 (99i:14058)
  • [Br99] M. Brion, Rational smoothness and fixed points of torus actions, Transf. Groups 4 (1999), 127-156. MR 1712861 (2000f:14072)
  • [C94] J. Carrell, The Bruhat graph of a Coxeter group, a conjecture of Deodhar, and rational smoothness of Schubert varieties, Proc. Symp. Pure Math. 56 (1994), 53-61. MR 1278700 (95d:14051)
  • [H09] A. Hultman, Criteria for rational smoothness of some symmetric orbit closures, arXiv:math.RT/0907.0936v1.
  • [LS90] V. Lakshmibai and B. Sandhya, Criterion for smoothness of Schubert varieties in $ SL(n)/B$, Proc. Indian Acad. Sci. 100 (1990), 45-52. MR 1051089 (91c:14061)
  • [MO88] T. Matsuki and T. Oshima, Embedding of discrete series into principal series, in The Orbit Method in Representation Theory, Progress in Math. 82, Birkhäuser, Boston, 1988, 147-175. MR 1095345 (92d:22020)
  • [M07] W. McGovern, Closures of $ K$-orbits in the flag variety for $ U(p,q)$, J. Alg. 322 (2009), 2709-2712. MR 2559857
  • [MT08] W. McGovern and P. Trapa, Pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety, J. Alg. 322 (2009), 2713-2730. MR 2559858
  • [P82] R. Proctor, Classical Bruhat orders are lexicographic shellable, J. Alg. 77 (1982), 104-126. MR 665167 (84j:20044)
  • [RS90] R. W. Richardson and T. A. Springer, On the Bruhat order for symmetric varieties, Geom. Dedicata 35 (1990), 389-436. MR 1066573 (92e:20032)

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 22E47, 57S25

Retrieve articles in all journals with MSC (2010): 22E47, 57S25


Additional Information

William M. McGovern
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-0001
Email: mcgovern@math.washington.edu

DOI: https://doi.org/10.1090/S1088-4165-2011-00386-1
Keywords: Flag variety, pattern avoidance, rational smoothness
Received by editor(s): January 28, 2010
Received by editor(s) in revised form: April 13, 2010, and May 26, 2010
Published electronically: July 12, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society