
arXiv: 2006.06575
We study normal reflection subgroups of complex reflection groups. Our point of view leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating function for fixed-space dimension over a reflection group is a product of linear factors involving generalized exponents. Our refinement gives a uniform proof and generalization of a recent theorem of the second author.
10 pages; to appear in DMTCS Proceedings (Formal Power Series and Algebraic Combinatorics)
normal subgroup, 20F55, 05E10, Combinatorial aspects of groups and algebras, Reflection and Coxeter groups (group-theoretic aspects), FOS: Mathematics, Mathematics - Combinatorics, exponents, Combinatorics (math.CO), Representation Theory (math.RT), reflection group, Mathematics - Representation Theory, exterior algebra
normal subgroup, 20F55, 05E10, Combinatorial aspects of groups and algebras, Reflection and Coxeter groups (group-theoretic aspects), FOS: Mathematics, Mathematics - Combinatorics, exponents, Combinatorics (math.CO), Representation Theory (math.RT), reflection group, Mathematics - Representation Theory, exterior algebra
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