This paper is the first in a series that describe a conjectural analog of the geometric Satake isomorphism for an affine Kac-Moody group (in this paper for simplicity we consider only untwisted and simply connected case). The usual geometric Satake isomorphism for a reductive group G identifies the tensor category Rep(G) of finitedimensional representations of the Langlands dual group G with th...

(Received for publication, June 18, 1957) The present investigation aims to know how hypothermia affects the secretion of 17-hydroxycorticosteroids of the adrenal glands in non-anesthetized dogs. The experiments were performed in 5 dogs. The adrenal venous blood was collected by the lumbar route method of Satake, Sugawara and Watanabe1), without anesthetizing or even fastening the animals. The ...

We provide a few natural applications of the analytic newvectors, initiated in \cite{JN} arXiv:1911.01880, to some questions automorphic forms for $\mathrm{PGL}_n(\mathbb{Z})$ with $n\ge 2$, archimedean conductor aspect. prove an orthogonality result Fourier coefficients, density estimate non-tempered forms, equidistribution Satake parameters respect Sato--Tate measure, and second moment centra...

Abstract We identify a geometric relation between the Laplace–Beltrami spectra and eigenfunctions on compact Riemannian symmetric spaces Borel–Weil theory using ideas from symplectic geometry quantization. This is done by associating with each space, via Marsden–Weinstein reduction, generalized flag manifold that covers space parametrizing all of its maximal totally geodesic tori. In process, w...