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Determinants of Representations of Coxeter Groups. (arXiv:1710.03039v1 [math.RT])
来源于:arXiv
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. 查看全文>>