Geodesic
A type \(B\) analogue of the category of finite sets with surjections
Nicholas Proudfoot1
1University of Oregon
The electronic journal of combinatorics, Tome 29 (2022) no. 3
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We define a type B analogue of the category of finite sets with surjections, and we study the representation theory of this category. We show that the opposite category is quasi-Gröbner, which implies that submodules of finitely generated modules are again finitely generated. We prove that the generating functions of finitely generated modules have certain prescribed poles, and we obtain restrictions on the representations of type B Coxeter groups that can appear in such modules. Our main example is a module that categorifies the degree i Kazhdan–Lusztig coefficients of type B Coxeter arrangements.
DOI : 10.37236/11186
Classification : 18B99, 05E10, 20F55

Nicholas Proudfoot  1

1 University of Oregon 
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Nicholas  Proudfoot. A type \(B\) analogue of the category of finite sets with surjections. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/11186

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