Automorph.isms and generalized involution models of finite complex reflection groups

作者：Marberg Eric^*

来源：Journal of Algebra, 2011, 334(1): 295-320.

DOI：10.1016/j.jalgebra.2011.02.021

• Complex reflection group
• Coxeter group
• Model
• Generalized involution model
• Gelfand model
• Automorphism

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 rip 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.

• 出版日期2011-5-15