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### 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, ...

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### 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 ...

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### 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 ...

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### 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
...