Geometry of \(G/P\). IX: The group \(SO(2n)\) and the involution \(\sigma\). (English) Zbl 0698.14058
[For part VIII of this series see ibid. 108, 435-471 (1988; Zbl 0618.14027).]
This is another paper in the long series of papers on standard monomial theory. For the groups \(SO(2n)\) an explicit description is obtained of the singular loci of Schubert varieties. Among the applications is a characterization of those Schubert varieties which are equal to the set of \(\sigma\)-invariants of their counterparts for \(SL(2n\)), \(\sigma\) being the involution of \(SL(2n)\) defining \(SO(2n)\).
This is another paper in the long series of papers on standard monomial theory. For the groups \(SO(2n)\) an explicit description is obtained of the singular loci of Schubert varieties. Among the applications is a characterization of those Schubert varieties which are equal to the set of \(\sigma\)-invariants of their counterparts for \(SL(2n\)), \(\sigma\) being the involution of \(SL(2n)\) defining \(SO(2n)\).
Reviewer: H.H.Andersen
MSC:
| 14M17 | Homogeneous spaces and generalizations |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
| 20G05 | Representation theory for linear algebraic groups |
| 20G15 | Linear algebraic groups over arbitrary fields |
Citations:
Zbl 0618.14027References:
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