The Hurwitz action in complex reflection groups
نویسندگان
چکیده
We enumerate Hurwitz orbits of shortest reflection factorizations an arbitrary element in the infinite family $G(m, p, n)$ complex groups. As a consequence, we characterize elements for which action is transitive and give simple criterion to tell when two belong same orbit. also quasi-Coxeter (those with factorization that generates whole group) n)$.
منابع مشابه
Automorphisms of complex reflection groups
I. MARIN AND J. MICHEL Abstract. Let G ⊂ GL(Cr) be an irreducible finite complex reflection group. We show that (apart from the exception G = S6) any automorphism of G is the product of an automorphism induced by tensoring by a linear character, of an automorphism induced by an element of NGL(Cr)(G) and of what we call a “Galois” automorphism: we show that Gal(K/Q), where K is the field of defi...
متن کاملHurwitz Groups and Surfaces
Hurwitz not only gave an upper bound for the number of automorphisms of a compact Riemann surface of genus greater than 2, but also gave a characterization of which finite groups could be groups of automorphisms achieving this bound. In practice, however, the identification of such groups and of the surfaces they act on is difficult except in special cases. We survey what is known. 1. How I Got...
متن کاملFusion Algebras for Imprimitive Complex Reflection Groups
We prove that the Fourier matrices for the imprimitive complex reflection groups introduced by Malle in [9] define fusion algebras with not necessarily positive but integer structure constants. Hence they define Z-algebras. As a result, we obtain that all known Fourier matrices belonging to spetses define algebras with integer structure constants.
متن کاملSpringer Theory for Complex Reflection Groups
Many complex reflection groups behave as though they were the Weyl groups of “nonexistent algebraic groups”: one can associate to them various representation-theoretic structures and carry out calculations that appear to describe the geometry and representation theory of an unknown object. This paper is a survey of a project to understand the geometry of the “unipotent variety” of a complex ref...
متن کاملSutherland Models for Complex Reflection Groups
There are known to be integrable Sutherland models associated to every real root system – or, which is almost equivalent, to every real reflection group. Real reflection groups are special cases of complex reflection groups. In this paper we associate certain integrable Sutherland models to the classical family of complex reflection groups. Internal degrees of freedom are introduced, defining d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Combinatorial theory
سال: 2022
ISSN: ['2766-1334']
DOI: https://doi.org/10.5070/c62156884