Richard Penney

Abstract Plancherel theorems and a Frobenius reciprocity theorem

Abstract A method for obtaining Plancherel theorems for unitary representations of Lie groups via C ∞ vector techniques is studied. The results are used to prove the nonunimodular Plancherel theorem of Moore and to study its convergence. A C ∞ Frobenius reciprocity theorem which generalizes Gelfands duality theorem is also proven.

Geometric Theory of Neutrinos

It is shown that the conditions Rμμ=0, R00≥0, RαβRβλ=14RρτRρτδαλ, Rαβ|σ=(RρτRρτ)|σRαβ, in the limit that the scalar RαβRαβ vanishes, reproduce the physics of neutrinos. That is, these conditions ensure the existence of a two‐component spinor which obeys the Weyl equation and represents a field of completely polarized neutrinos.

Duality Invariance and Riemannian Geometry

It is shown that the postulate of indistinguishability of the Maxwell field tensor from its dual leads to the concept of the electromagnetic field tensor as a spinor component in dual space. The demand for algebraic consistency dictates a unique connection with the gravitational field. The Maxwell field must be viewed as a set of potentials, and the necessity for a duality gauge condition excludes the existence of magnetic monopoles.

CANONICAL OBJECTS IN KIRILLOV THEORY ON NILPOTENT LIE GROUPS

It is shown that to each element / in the dual space of the Lie algebra of a nilpotent Lie group there is a uniquely defined subgroup Kx for which the representation corresponding to / is inducible from a square- integrable-modulo-its-kernel representation of Kx .

Norms of Hadamard Multipliers

For

Non-elliptic Laplace equations on nilpotent Lie groups

B

Ground states of the antiferromagnetic Ising model on finite triangular lattices of simple shape

a fixed matrix, the authors consider the problem of finding the norm of the map

Self-dual cones in Hilbert space

X \mapsto X \bullet B

Tensorial Description of Neutrinos

, where

Lie cohomology of representations of nilpotent Lie groups and holomorphically induced representations

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