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arXiv · 1710.03039

Determinants of Representations of Coxeter Groups

Debarun Ghosh·Steven Spallone
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Abstract

In [APS], the authors characterize the partitions of $n$ whose corresponding representations of $S_n$ have nontrivial determinant. The present paper extends this work to all irreducible finite Coxeter groups $W$. Namely, given a nontrivial multiplicative character $\omega$ of $W$, we give a closed formula for the number of irreducible representations of $W$ with determinant $\omega$. For Coxeter groups of type $B_n$ and $D_n$, this is accomplished by characterizing the bipartitions associated to such representations.

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BibTeXRIS

Debarun Ghosh, Steven Spallone. 2017-10-09. Determinants of Representations of Coxeter Groups. https://arxiv.org/abs/1710.03039

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