Stasinski and Voll’s Hyperoctahedral Group Conjecture
نویسنده
چکیده
In a recent paper, Stasinski and Voll introduced a length-like statistic on hyperoctahedral groups and conjectured a product formula for this statistic’s signed distribution over arbitrary descent classes. Stasinski and Voll proved this conjecture for a few special types of parabolic quotients. We prove this conjecture in full, showing it holds for all parabolic quotients. In the case that the descent class is a singleton, this formula gives the Poincaré polynomials for the varieties of symmetric matrices of a fixed rank.
منابع مشابه
A New Statistic on the Hyperoctahedral Groups
We introduce a new statistic on the hyperoctahedral groups (Coxeter groups of type B), and give a conjectural formula for its signed distributions over arbitrary descent classes. The statistic is analogous to the classical Coxeter length function, and features a parity condition. For descent classes which are singletons the conjectured formula gives the Poincaré polynomials of the varieties of ...
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