Unitary Subgroups Research Articles

On periods of CUSP forms and algebraic cycles forU(3)

In this paper we discuss relations between the following types of conditions on a representationπ in a cuspidalL-packet ofU(3): (1)L(s, π×ξ) has a pole ats=1 for someξ; (2) aperiod ofπ over some algebraic cycle inU(3) (coming from a unitary group in two variables) is non-zero; and (3) π is atheta-series lifting from some unitary group in two variables. As an application of our analysis, we show that the algebraic cycles on theU(3) Shimura variety arenot spanned (over the Hecke algebra) by the modular and Shimura curves coming from unitary subgroups.

Erratum: Double coset analysis for symmetry adapting Nth rank tensors of U (n) to its unitary subgroups

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Double coset analysis for symmetry adapting Nth rank tensors of U (n) to its unitary subgroups

Representations of the unitary group U (n) symmetry adapted to the subgroup sequences U (n) U(nj)U(in) U (inj) are considered using double coset decomposition. The matrix elements of the double coset representatives are related to identical coefficients developed

Finite Transformations and Basis States of SU(n)

A convenient parameterization for finite transformations of SU(n) is developed which explicitly exhibits the special unitary subgroups. This is also used to parameterize the defining space. Higher-dimensional representations are discussed. The question of which representations carry the trivial representation of SU(n − 1) is considered, as well as the parameterization of these states. Application is made to the transformations and basis states of SU(3).