Automorphisms and Generalized Involution Models of Finite Complex Reflection Groups

Details Automorphisms and Generalized Involution Models of Finite Complex Reflection Groups Automorphisms and Generalized Involution Models of Finite Complex Reflection Groups

2010-07-28

arxiv.org/abs/1007.4886v4

J. Algebra 334 (2011), 295-320

Mathematics

Representation Theory

29 pages

Scientific paper

10.1016/j.jalgebra.2011.02.021

We prove that a finite complex reflection group has a generalized involution model, as defined by Bump and Ginzburg, if and only if each of its irreducible factors is either $G(r,p,n)$ with $\gcd(p,n)=1$; $G(r,p,2)$ with $r/p$ odd; or $G_{23}$, the Coxeter group of type $H_3$. We additionally provide explicit formulas for all automorphisms of $G(r,p,n)$, and construct new Gelfand models for the groups $G(r,p,n)$ with $\gcd(p,n)=1$.

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