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Results tagged with rt.representation-theory
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user 13215
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
1
vote
Status of a conjectural definition of H. Nakajima
The following paper might help get you up to date, by working through its references:
Yoshiyuki Kimura, Fan Qin. Graded quiver varieties, quantum cluster algebras and dual canonical basis.
http:/ …
- 2,218
12
votes
Accepted
Classification of modules all whose weight spaces are $1$-dimensional
The following result of Howe [Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond] answers this completely:
Let $\mathfrak{g}$ be a finite-dimensional simple complex …
- 2,218
15
votes
Accepted
Which cluster algebras have been categorified?
There are several different questions in here and what follows are only partial answers to some of these, mostly consisting of pointers to pieces of the literature.
"In what other instances have clu …
- 2,218
10
votes
Accepted
What do cluster algebras tell us about Grassmannians?
I'm afraid that as far as I know, the answer is no. That is, the cluster structure hasn't (yet) told us anything new. There are two reasons why we might have expected that, though.
Firstly, the G …
- 2,218
9
votes
Is it possible that the GHKK canonical basis for cluster algebras is the Lusztig/Kashiwara d...
Quoting from
Geiss, Christof; Leclerc, Bernard; Schröer, Jan, Preprojective algebras and cluster algebras.,
First, the cluster algebra structure, when it is known, is usually wellhidden, and its d …
- 2,218