9
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What are global sections of the determinant bundle on the Beilinson-Drinfeld Grassmannian?
In a recent paper https://arxiv.org/abs/2003.12930 the space of global sections on Schubert subvarietis of Beilinson-Drinfeld Grassmanian was computed. It turns out to be global Demazure module over ...
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5
votes
The affine Grassmannian and the Bogomolny equations
For those who could be interested, I worked out a formal construction of the E3-structure on the derived Satake category here, following the arguments hinted at by Lurie.
- 405
4
votes
Reconciling the affine grassmannian and the based loop group
There are many spaces of maps $S^1\to K$ (hence many version of the affine Grassmannian) one might want to consider.
Let's list them:
• Algebraic maps (i.e. algebraic maps from $\mathbb C^\times$ to $...
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4
votes
Accepted
Drinfeld Sokolov and the semiinfinite flag variety
Maybe let me try to synthesize my comments into an answer. All of this is contained in Raskin's beautiful paper arxiv.org/abs/1611.04937 on Whittaker categories. Convention: We work here in the ...
- 5,888
4
votes
Accepted
how to view homology of affine Grassmannian as a subring of symmetric function
You should look at the book of Lam, Lapointe, Morse, Schilling, Shimozono and Zabrocki. More specifically, under k-Schur functions and how/why they constitute a basis of $H_*(Gr_{SL_k})$. They mainly ...
- 206
3
votes
Affine vs Yokonuma
I am not entirely sure if this is the kind of answer you are looking for, but Chlouveraki in her thesis as well as here explains the differences in the two deformations. Generally speaking, in the ...
- 206
3
votes
Relation between affine flag and Grassmannian Steinberg variety
To clarify the issue you're having: you can look at the spaces
$$\mathcal{\tilde{R}}=\{(x,g)\in \mathfrak{g}(\mathcal{O})\times G((t)) \mid \mathrm{Ad}_{g^{-1}}(x)\in \mathfrak{g}(\mathcal{O})\}$$
$$\...
- 44k
2
votes
Cartan decomposition of loop group
Apparently, this is based on a result by Iwahori and Matsumoto (Corollary 2.17 of [IM]). A modern proof of this result can be found on [DHLH]. This result is one of the main elements of the proof of ...
- 543
2
votes
Relation between affine flag and Grassmannian Steinberg variety
Sorry, this question itself is wrong!
Bezrukavnikov-Finkelberg-Mirković actually showed that the $G(\mathcal{O})$-equivariant $K$-theory of affine Grassmannian Steinberg variety $\mathcal{R} = \{ (x,...
- 2,273
2
votes
Accepted
Homological contractibility of a prestack
This is proven in some detail in section 3 Gaitsgory's writeup of his the Atiyah-Bott formula. He starts with the fully faithfulness definition, then proves the equivalance with homological statement ...
- 2,277
2
votes
Accepted
A technical question about affine grassmanian
I am being told it is better not to leave answers in comments. So:
I think you can find more details in Martin Kreidl's thesis, available at uni-due.de/~hx0051/Dissertation.pdf.
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