Orthogonal Group Matrices of Hyperoctahedral Groups
نویسندگان
چکیده
منابع مشابه
The Hyperoctahedral Quantum Group
We present a definition for free quantum groups. The idea is that these must satisfy S n ⊂ G ⊂ U + n , along with a technical representation theory condition. We work out in detail the case of quantum analogues of the hyperoctahedral group Hn. We first consider the hypercube in R , and show that its quantum symmetry group is in fact a q-deformation of On at q = −1. Then we consider the space fo...
متن کاملA 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 ...
متن کاملThe absolute order on the hyperoctahedral group
The absolute order on the hyperoctahedral group Bn is investigated. Using a poset fiber theorem, it is proved that the order ideal of this poset generated by the Coxeter elements is homotopy Cohen–Macaulay. This method results in a new proof of Cohen–Macaulayness of the absolute order on the symmetric group. Moreover, it is shown that every closed interval in the absolute order on Bn is shellab...
متن کاملTransitive Factorizations in the Hyperoctahedral Group
The classical Hurwitz Enumeration Problem has a presentation in terms of transitive factorisations in the symmetric group. This presentation suggests a generalization from type A to other £nite re¤ection groups and, in particular, to type B. We study this generalization both from a combinatorial and a geometric point of view, with the prospect of providing a means of understanding more of the s...
متن کاملSigned Excedance Enumeration in the Hyperoctahedral group
Several signed excedance-like statistics have nice formulae or generating functions when summed over the symmetric group and over its subset of derangements. We give counterparts of some of these results when we sum over the hyperoctahedral group and its subset of derangements. Our results motivate us to define and derive attractive bivariate formulae which generalise some of these results for ...
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: Nagoya Mathematical Journal
سال: 1966
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000026404