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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} …

First note that there is the book of Vogan (Representation Theory if real reductive groups) which discusses the case of $SL_2(\mathbb{R})$ on a very basic level. I think this is a good start. In my o …

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 …

Geometric respectively topological methods are widely applied in representation theory. As far as I know mainly cohomological methods are used. I wonder if there are concrete applications of the …

The point is following: $\overline{Gr^\lambda}$ is a finite dimensional variety acted upon by the pro-algebraic group $G(\mathbb{C}[[t]])$. This action factors through the action of some finite dim …

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 $\ …

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 …

Setup: Let $\mathcal{K}=\mathbb{C}((t))$, $\mathcal{O}:= \mathbb{C}[[t]]$ and $G$ be a reductive algebraic group (over $\mathbb{C}$). Let further $\mathcal{K}_n$ denote the $\mathcal{O}$-ideal in $\m …

Let $G$ be a complex reductive group, $L\subset G$ a Levi subgroup and $Rep(G)$ the category of rational representations of $G$. My Question: What is the geometric analogue of the restriction f …

This may be a little bit lazy but the statement you want is given on page 227 in [Lu]. The proof is given on page 228. [Lu]=Lusztig, George Singularities, character formulas, and a q-analog of weigh …

I hope this question is not too vague. Let $G$ be a complex reductive group, $B$ a Borel subgroup of $G$, and $P$ a parabolic containing $B$. Denote by $\pi:G/B\to G/P$ the canonical map. Consider th …

I hope this question has not been asked before. I would like to know which Ideas led (Deligne), Kazhdan and Lusztig believe, that Kazhdan–Lusztig polynomials can be expressed via intersection cohom …

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 …

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 …