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Results tagged with rt.representation-theory
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user 16002
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
5
votes
0
answers
226
views
Is there a brief name for the symmetric space $SL_{2n} / Sp_{2n}$?
Let $V$ be a complex vector space of even dimension. Then the homogeneous space $SL_{2n}(V) / SP_{2n}(V)$ is known to parametrize the space of non-degenerate skew-symmetric bilinear forms on $V$.
(1 …
6
votes
Cohomology ring of a flag variety and representation theory
Both the study of ordinary Schubert calculus (the ordinary, e.g. Borel-Moore, cohomology of Schubert varieties of the flag variety) and the study of Kazhdan-Lusztig theory (the intersection cohomology …
- 1,780
2
votes
Covering relations in $K\backslash G/B$
While the paper of Richardson-Springer does study the weak order, it also has useful results on the usual (strong) Bruhat order. In particular, Theorem 7.11 says that Bruhat order is characterized as …
- 1,780
3
votes
Accepted
Dimension of spaces of invariants/tableaux functions
The numbers you refer to are known as Kostka numbers. They are discussed in standard references like Fulton's Young Tableaux and Stanley's Enumerative Combinatorics. The weights of a tableaux are of …
- 1,780
7
votes
Accepted
Uniqueness of the wonderful compactification of a semi-simple group
I assume you mean the variety $G$ considered as a $G \times G$ variety via the action $(g,h) \cdot x = gxh^{-1}$, which is the standard interpretation in the literature. The variety $G$ is spherical a …
- 1,780