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Results tagged with reference-request
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user 16002
This tag is used if a reference is needed in a paper or textbook on a specific result.
1
vote
Reference for finite number of Weyl groups of reductive groups of rank $r$
A Weyl group is a crystallographic finite reflection group, i.e. it is a finite group generated by reflections in Euclidean space that preserves a lattice in the Euclidean space. So it suffices to pr …
- 1,780
7
votes
References request on the algebraic geometry of projective homogeneous spaces
Michel Brion's Lectures on the Geometry of Flag Varieties answers all of your questions in the special case $G = SL_n$ and $P = B$ (the Borel subgroup of upper triangular matrices). See Section 1.4. …
- 1,780
1
vote
Theory of cones
If you are interested in the lattice point enumeration aspect, I'd also suggest Computing the Continuous Discretely by Beck and Robins. There's a version of the book available on their website which …
5
votes
0
answers
226
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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 …
3
votes
Is there a standard name for this poset
This is a manifestation of the Bruhat order on the Grassmannian $Gr(k,n)$ of $k$-planes in an $n$-dimensional vector space.
In terms of partitions (Young diagrams):
Given a set $X$ as above, let $\la …
- 1,780
4
votes
Accepted
Intersection theory for $G$-varieties - an action on the chow ring?
If you are interested in intersection theory of varieties with $G$-actions, then you want to study equivariant intersection theory. This theory exploits the $G$-action in a way that leads to deeper i …
- 1,780
4
votes
RSK and crystal operators
There is a detailed analysis in Chapters 7 and 8 of Bump and Schilling's Crystal Bases. They work through the connection between RSK and crystals in careful detail, though I don't recall how much deta …
- 1,780
2
votes
Bruhat order and Schubert cycles
The result is stated and proved as Corollary 2.2.2 of Michel Brion's Lectures on the Geometry of Flag Varieties.
- 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
3
votes
Reading list for Equivariant Cohomology
Some additional resources, which are more on the algebraic side than the symplectic side:
1) Bill Fulton's Eilenberg lectures on Equivariant Cohomology in Algebraic Geometry, available at David Ander …
- 1,780