(U(p, q), U(p − 1, q)) is a generalized Gelfand pair

Draft #1 On a (β, q)-generalized Fisher information and inequalities involving q-Gaussian distributions

In the present paper, we would like to draw attention to a possible generalized Fisher information that ts well in the formalism of nonextensive thermostatistics. This generalized Fisher information is de ned for densities on R. Just as the maximum Rényi or Tsallis entropy subject to an elliptic moment constraint is a generalized qGaussian, we show that the minimization of the generalized Fishe...

The generalized Gelfand – Graev characters of GL n ( F q ) ( extended abstract )

Introduced by Kawanaka in order to find the unipotent representations of finite groups of Lie type, generalized Gelfand–Graev characters have remained somewhat mysterious. Even in the case of the finite general linear groups, the combinatorics of their decompositions has not been worked out. This paper re-interprets Kawanaka’s definition in type A in a way that gives far more flexibility in com...

PRESENTING GENERALIZED q - SCHUR

Generalized Q-functions

The modulus squared of a class of wave functions defined on phase space is used to define a generalized family of Q or Husimi functions. A parameter λ specifies orderings in a mapping from the operator |ψ〉〈σ| to the corresponding phase space wave function, where σ is a given fiducial vector. The choice λ = 0 specifies the Weyl mapping and the Q-function so obtained is the usual one when |σ〉 is ...

GENERALIZED q - FIBONACCI NUMBERS

We introduce two sets of permutations of {1, 2, . . . , n} whose cardinalities are generalized Fibonacci numbers. Then we introduce the generalized q-Fibonacci polynomials and the generalized q-Fibonacci numbers (of first and second kind) by means of the major index statistic on the introduced sets of permutations.