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A note on trilinear forms for reducible representations and Beilinson's conjectures

Michael Harris, Anthony Scholl (2001)

Journal of the European Mathematical Society

We extend Prasad’s results on the existence of trilinear forms on representations of G L 2 of a local field, by permitting one or more of the representations to be reducible principal series, with infinite-dimensional irreducible quotient. We apply this in a global setting to compute (unconditionally) the dimensions of the subspaces of motivic cohomology of the product of two modular curves constructed by Beilinson.

A Paley-Wiener theorem for step two nilpotent Lie groups.

Sundaram Thangavelu (1994)

Revista Matemática Iberoamericana

It is an interesting open problem to establish Paley-Wiener theorems for general nilpotent Lie groups. The aim of this paper is to prove one such theorem for step two nilpotent Lie groups which is analogous to the Paley-Wiener theorem for the Heisenberg group proved in [4].

A Paley-Wiener theorem on NA harmonic spaces

Francesca Astengo, Bianca di Blasio (1999)

Colloquium Mathematicae

Let N be an H-type group and consider its one-dimensional solvable extension NA, equipped with a suitable left-invariant Riemannian metric. We prove a Paley-Wiener theorem for nonradial functions on NA supported in a set whose boundary is a horocycle of the form Na, a ∈ A.

A remarkable contraction of semisimple Lie algebras

Dmitri I. Panyushev, Oksana S. Yakimova (2012)

Annales de l’institut Fourier

Recently, E.Feigin introduced a very interesting contraction 𝔮 of a semisimple Lie algebra 𝔤 (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic properties of 𝔤 . For instance, the algebras of invariants of both adjoint and coadjoint representations of 𝔮 are free, and also the enveloping algebra of 𝔮 is a free module over its centre.

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