Discrete series for an affine symmetric space
نویسندگان
چکیده
منابع مشابه
Affine Stanley Symmetric Functions
We define a new family F̃w(X) of generating functions for w ∈ S̃n which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions such as their symmetry and conjecture certain positivity properties. As an application, we relate these functions to the k-Schur functions of Lapointe, Lascoux and Morse as well as the cylindric Schur functions of Postnikov. ...
متن کاملAffine Stanley symmetric functions for classical types
We introduce affine Stanley symmetric functions for the special orthogonal groups, a class of symmetric functions that model the cohomology of the affine Grassmannian, continuing the work of Lam and Lam, Schilling, and Shimozono on the special linear and symplectic groups, respectively. For the odd orthogonal groups, a Hopf-algebra isomorphism is given, identifying (co)homology Schubert classes...
متن کاملAn Ideal Separating Extension of Affine Space
In affine space the set of solutions to a system of polynomial equations does not uniquely determine the system. We extend affine space so that the solutions (in the extension) to a system of equations uniquely determines the system. 1. Statement of the problem In particular, for field R let elements of R[x] = R[x1, ..., xn] act on the set of power series R[[T ]] = R[[T1, ..., Tn]] by way of th...
متن کاملMore On Embedding an Affine Space in a Vector Space
for all a1 . . . , am ∈ E, all v1, . . . , vm ∈ −→E , and all λ1, . . . , λm ∈ R. Furthermore, for λi = 0, 1 ≤ i ≤ m, we have f̂(v1 +̂ λ1a1, . . . , vm +̂ λmam) = λ1 · · ·λmf(a1 + λ−1 1 v1, . . . , am + λ−1 m vm). Proof . Let us assume that f̂ exists. We first prove by induction on k, 1 ≤ k ≤ m, that f̂(a1, . . . , vi1 , . . . , vik , . . . , am) = fS(vi1 , . . . , vik), for every S ⊆ {1, . . . ,m},...
متن کاملDiscrete Affine Wavelet Transforms
In this paper we show that discrete affine wavelet transforms can provide a tool for the analysis and synthesis of standard feedforward neural networks. It is shown that wavelet frames for L2(IR) can be constructed based upon sigmoids. The spatia-spectral localization property of wavelets can be exploited in defining the topology and determining the weights of a feedforward network. Training a ...
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: Hiroshima Mathematical Journal
سال: 1981
ISSN: 0018-2079
DOI: 10.32917/hmj/1206134218