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pro vyhledávání: '"Wallach, Nolan R."'
Autor:
Wallach, Nolan R.
This paper, in particular, gives a complete proof of the direct integral version of the Whittaker Plancherel Theorem. The main emphasis is on certain Hilbert and Fr\'echet vector bundles over a space that has a submersion onto the tempered dual. This
Externí odkaz:
http://arxiv.org/abs/2410.23226
Autor:
Wallach, Nolan R.
In this paper the spherical case of the Whittaker Inversion Theorem is given a relatively self-contained proof. This special case can be used as a help in deciphering the handling of the continuous spectrum in the proof of the full theorem. It also l
Externí odkaz:
http://arxiv.org/abs/2303.11256
Autor:
Wallach, Nolan R.
In his first 1958 paper on zonal spherical functions Harish-Chandra proved an extremely delicate convergence theorem which was basic to his subsequent definition of his Schwartz space and his theory of cusp forms. This paper gives elementary proofs t
Externí odkaz:
http://arxiv.org/abs/2206.14773
Autor:
Swanson, Joshua P., Wallach, Nolan R.
This paper studies three results that describe the structure of the super-coinvariant algebra of pseudo-reflection groups over a field of characteristic $0$. Our most general result determines the top component in total degree, which we prove for all
Externí odkaz:
http://arxiv.org/abs/2109.03407
Autor:
Wallach, Nolan R.
An interpretation of the Casselman-Wallach (C-W) Theorem is that the $K$-finite functor is an isomorphism of categories from the category of finitely generated, admissible smooth Fr\'echet modules of moderate growth to the category of Harish-Chandra
Externí odkaz:
http://arxiv.org/abs/2004.08391
Autor:
Swanson, Joshua P., Wallach, Nolan R.
We give a type-independent construction of an explicit basis for the semi-invariant harmonic differential forms of an arbitrary pseudo-reflection group in characteristic zero. Our "top-down" approach uses the methods of Cartan's exterior calculus and
Externí odkaz:
http://arxiv.org/abs/2001.06076
Autor:
Wallach, Nolan R.
The symmetric group acts on polynomial differential forms on $\mathbb{R}^{n}$ through its action by permuting the coordinates. In this paper the $S_{n}% $-invariants are shown to be freely generated by the elementary symmetric polynomials and their e
Externí odkaz:
http://arxiv.org/abs/1906.11787
Autor:
Wallach, Nolan R.
The first main result is that the Casselman-Wallach Globalization of a real analytic family of Harish-Chandra modules is continuous in the parameter. Our proof of this result uses results from the thesis of Vincent van der Noort in several critical w
Externí odkaz:
http://arxiv.org/abs/1902.01871
Autor:
Wallach, Nolan R.
The main result asserts: Let $G$ be a reductive, affine algebraic group and let $(\rho ,V)$ be a regular representation of $G$. Let $X$ be an irreducible $\mathbb{C}^{ \times } G$ invariant Zariski closed subset such that $G$ has a closed orbit that
Externí odkaz:
http://arxiv.org/abs/1811.07195