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I hope this question is not too unspecific: Can Soergel's Categorical Local Langlands conjectures [1] be interpreted as special form of geometric Langlands. I think this is somehow hidden in the wo …

I hope my answer is not a reproduction of Jeffrey Adams answer. (I dont have the book at hand) If I understand you right you want to know the indecomposable Harish-Chandra modules of $SL_2(\mathbb{R} …

One can also argue as follows: $G(\mathcal{O})$ operates transitivly on each stratum $\mathcal{G}^\lambda$. The isotropy group at $t^\lambda$ is $P^a_\lambda:= (t^\lambda)^{-1}G(\mathcal{O})t^\lambda …

Let $A$ and $B$ $dg$-algebras over $\mathbb{C}$. If there exists an isomorphism $f:A\to B$, then every subalgebra $A'$ of $A$ is isomorphic to the subalgebra $f(A')$ of $B$. What is if $f$ is onl …

I hope somebody can give me a good reference for the following: Let $G$ be a complex reductive group $H$ be a closed subgroup. Let further $R$ be any $\mathbb{C}$-algebra. Then the canonical map $$G …

I am sorry to give a bounty to such a crappy question but an answer would help me a lot. I am stuck with the following simple (i guess but) technical problem. Let $G$ be a complex reductive grou …

I allready asked this on MO, but did not get any answer. Given a finite quiver with relations. When is the path algebra modulo relations hereditary? If the path algebra is finite dimensional or th …

I do not really answer you question but maybe this helps: Let $\mathcal{K} =\mathbb{C}((t))$ and $\mathcal{O}:=\mathbb{C}[[t]]$. For $n\geq 0$ denote the $\mathcal{K}_n$ the $\mathcal{O}$ ideal in $\ …

The answer is yes $D^b_G(X)$ is equivariantly formal. The result has been proved in a diploma thesis written under the supervision of Wolfgang Soergel. (Unfortunately it is not available electronicall …

It's a while ago but I used to study the books: An Introduction to General Relativity, Hughston and Tod (1990) and General Relativity With Applications to Astrophysics , Straumann (2004) I remembe …

Let $G$ be an algebraic group (over $\mathbb{C}$) acting algebraically on a variety $X$. Bernstein and Lunts then define in [BL94] the equivariant derived category $D^b_G(X,\mathbb{C})$ (of $\mathbb{C …

Sorry for this question but I really have difficulties with model categories. Usually a $dg$-algebra $A$ is called formal, if there exists a $dg$-algebra $B$ and quasi-isomorphisms $$A\leftarrow B\to …

Let $G$ be a finite group and $\mathcal{A}$ be a $dg$-algebra. Assume $G$ acts on $\mathcal{A}$, i.e. there exists a homomorphism $G\to {\rm Aut}_{dg}(\mathcal{A})$. Assume further there exists a $dg …

Additionally to Peter Crooks answer I would recommend to study the book of Hotta and others : D-Modules, Perverse Sheaves, and Representation Theory Here you can learn about derived categories and pe …