Abstract We prove the Casselman–Shalika formula for unramified groups over a non-archimedean local field by studying action of spherical Hecke algebra on space compact Whittaker functions via twisted Satake transform. This method provides conceptual explanation appearance characters dual group in formula.

‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...

‎Hensel [K‎. ‎Hensel‎, ‎Deutsch‎. ‎Math‎. ‎Verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎Fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{Z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎Then $|x...

Copulas [18] link univariate marginal distribution functions into a joint distribution function of the corresponding random vector. In this paper we will deal with bivariate copulas only. Recall that a function C : [0, 1] → [0, 1] is a (bivariate) copula whenever it is grounded, C(x, y) = 0 whenever 0 ∈ {x, y}, it has neutral element 1, C(x, y) = x∧y, whenever 1 ∈ {x, y} and it is 2-increasing,...

In this paper, we compute the Hecke action of a certain test function on space an unramified principal series connected reductive group over non-archimedean local field. The key our computation is theory Iwahori–Hecke algebra. As application, obtain new expression L-functions representations.

Given a reductive group over complete non-Archimedean field, it is well known that techniques from analytic geometry provide an embedding of the corresponding Bruhat–Tits building into space associated with group; by composing maps to suitable proper spaces, this eventually leads various compactifications building. In present paper, we give intrinsic characterization embedding.

Efficient sampling algorithms for both exchangeable and nested Archimedean copulas are presented. First, efficient sampling algorithms for the nested Archimedean families of Ali-Mikhail-Haq, Frank, and Joe are introduced. Second, a general strategy how to build a nested Archimedean copula from a given Archimedean generator is presented. Sampling this copula involves sampling an exponentiallytil...

In this paper, a new algebraic representation by the non-Archimedean fields is proposed to model stratified/ranked knowledge bases. The non-Archimedean representation is in the form of the non-Archimedean polynomials. With the nonArchimedean representation, the most widely used ordering strategies are easily induced and compared. Moreover, a framework of prioritized merging operators using the ...