Open this publication in new window or tab >>2012 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 229, no 1, p. 183-200Article in journal (Refereed) Published
Abstract [en]
Let G be a connected reductive linear algebraic group over C with an involution theta. Denote by K the subgroup of fixed points. In certain cases, the K-orbits in the flag variety G/B are indexed by the twisted identities t = {theta(omega(-1))omega | omega is an element of W} in the Weyl group W. Under this assumption, we establish a criterion for rational smoothness of orbit closures which generalises classical results of Carrell and Peterson for Schubert varieties. That is, whether an orbit closure is rationally smooth at a given point can be determined by examining the degrees in a "Bruhat graph" whose vertices form a subset of t. Moreover, an orbit closure is rationally smooth everywhere if and only if its corresponding interval in the Bruhat order on t is rank symmetric. less thanbrgreater than less thanbrgreater thanIn the special case K = Sp(2n) (C), G = SL(2n) (C), we strengthen our criterion by showing that only the degree of a single vertex, the "bottom one", needs to be examined. This generalises a result of Deodhar for type A Schubert varieties.
Place, publisher, year, edition, pages
Elsevier, 2012
Keywords
Rational smoothness, Symmetric orbit closure, Bruhat graph
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-73094 (URN)10.1016/j.aim.2011.09.002 (DOI)000297184800007 ()
2011-12-162011-12-162017-12-08