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3
votes
0answers
41 views

Can Bruhat cells in semi simple groups be induced from matrices?

Let $G$ be a semisimple Lie group. Embed it as a subgroup into a special linear group of suitable rank, $SL(n)$ (real or complex). The question is: is it always possible to find such an embedding, ...
1
vote
1answer
209 views

Schubert problems to cycle class in Grassmanian

Say I have a family of linear spaces, and that I can solve all Schuber problems of that family (that is, how many members of the family pass through a set $S$ of linear spaces, where we consider all ...
13
votes
0answers
465 views

Comparing the Kazhdan-Lusztig and Steinberg pre-orders

Both Kazhdan-Lusztig and Steinberg have defined pairs of preorders on $S_n$. Kazhdan and Lusztig's preorders come from their basis: We write $x\leq_L y$ if any left ideal spanned by K-L basis ...
11
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1answer
974 views

Detailed proof of cup product equivalent to intersection

Consider a smooth, closed, compact finite-dim manifold. We have Poincare Duality to relate the cocycles and cycles. I would like to know where I can find a reference for a proof that the cup ...