منابع مشابه
Involutions of Iwahori-Hecke algebras and representations of fixed subalgebras
We establish branching rules between some Iwahori-Hecke algebra of type B and their subalgebras which are defined as fixed subalgebras by involutions including Goldman involution. The IwahoriHecke algebra of type D is one of such fixed subalgebras. We also obtain branching rules between those fixed subalgebras and their intersection subalgebra. We determine basic sets of irreducible representat...
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For a p-adic field F of characteristic zero, the embeddings of a tame supercuspidal representation π of G = GLn(F ) in the space of smooth functions on the set of symmetric matrices in G are determined. It is shown that the space of such embeddings is nonzero precisely when −1 is in the kernel of π and, in this case, this space has dimension four. In addition, the space of H-invariant linear fo...
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Let L be a lattice in d-dimensional real Euclidean space V , and let σ be a polyhedral decomposition of V . If the cones of σ are generated by vectors in L, σ is called a (complete) fan in L (and we say σ is integral with respect to L). If each i-dimensional cone of σ is generated by i vectors, we say σ is simplicial. Associated to any fan σ in V is a toric variety, Xσ. In [7], Stembridge showe...
متن کاملPermutation statistics on involutions
In this paper we look at polynomials arising from statistics on the classes of involutions, In, and involutions with no fixed points, Jn, in the symmetric group. Our results are motivated by F. Brenti’s conjecture [3] which states that the Eulerian distribution of In is logconcave. Symmetry of the generating functions is shown for the statistics d, maj and the joint distribution (d, maj). We sh...
متن کاملA Statistic on Involutions
We define a statistic, called weight, on involutions and consider two applications in which this statistic arises. Let I (n)denote the set of all involutions on [n](= {1, 2, . . . , n}) and let F(2n)denote the set of all fixed point free involutions on [2n]. For an involution δ, let |δ| denote the number of 2-cycles in δ. Let [n]q = 1+q+· · ·+qn−1 and let (k)q denote the q-binomial coefficient....
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.03.023