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Results tagged with rt.representation-theory
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user 6771
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
16
votes
Accepted
Is there a short proof that the Kostka number $K_{\lambda \mu}$ is non-zero whenever $\lambd...
I think the following is a simple combinatorial argument which constructs the most dominant semistandard $\lambda$-tableau of content $\mu$ whenever $\lambda\trianglerighteq\mu$. (n.b. I haven't foll …
- 1,570
14
votes
Accepted
Dual of a Specht module
Yes, this works over $\mathbb Z$, and the pairing can be explicitly realised with polytabloids. See Section 4 of my paper "On the structure of Specht modules", J. London Math. Soc. 67 (2003) 85–102. ( …
- 1,570
8
votes
Accepted
What is the most general "two in one row for A & in one column for B" theorem?
I can't give you your desired "most general" theorem, but I can say a little about this. In (b), the condition "shape(A) is lexicographically larger than shape(B)" is much stronger than it needs to be …
- 1,570
1
vote
Accepted
Reference for the action of the Mullineux involution on a partition with an added good node
The equivalence of Kleshchev's algorithm and Mullineux's algorithm was proved by Ford and Kleshchev, but the result they prove is slightly weaker than you want. The result you're asking for is Coroll …
- 1,570