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2 votes
0 answers
96 views

Morita equivalence between category of modules of hyperoctahedral group with the category of modules of direct product of two symmetric groups

I am reading the paper "R. Dipper and G. D. James, Representations of Hecke algebras of type $B_n$, J. Algebra (146) 1992, 454–481". Theorem 4.18 says that the category of modules of the ...
noone 's user avatar
  • 179
3 votes
0 answers
311 views

What is known about representations of $S_n$ in other categories?

Is anything known about representations of the symmetric group $S_n$ for categories other than $\textbf{Vect}_k$, vector spaces and linear maps over a field $k$. That is, a group $G$ can be considered ...
Jackson Walters's user avatar
3 votes
0 answers
155 views

Braid 2-groups, symmetric 2-groups

Is there an object which can be called a "braid 2-group"? Or a "symmetric 2-group"? (Note: not a braided 2-group) I am ignorant about 2-categories but I hope that a good candidate ...
Alex Ogg's user avatar
  • 169
9 votes
1 answer
424 views

What is this symmetric simplex category, concretely?

Let $\Delta_+$ denote the category of finite ordinal numbers with monotonic maps (the subscript indicates that $0$ is included, so this is the augmented simplex category). This has a monoidal ...
HeinrichD's user avatar
  • 5,482
8 votes
1 answer
2k views

What is a Specht module?

I'm studying the structure of the Specht module for $S_n$ and I would like to know if there is some generalizations of this structure for Weyls groups or Coxeter groups. Also, I'm interest to know ...
Yannic's user avatar
  • 527