Let k be a local field of characteristic zero. Let π be an irreducible admissible smooth representation of GL 2n (k). We prove that for all but countably many characters χ of GL n (k)×GL n (k), the space of χ-equivariant (continuous in the archimedean case) linear functionals on π is at most one dimensional. Using this, we prove the uniqueness of twisted Shalika models.2000 Mathematics Subject Classification. 22E50.

In this paper, we classify the irreducible integrable modules with finite dimensional weight spaces and non-trivial g c -action for the nullity 2 toroidal extended affine Lie algebra g, where g c is the core of g.2010 Mathematics Subject Classification. 22E50.

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Abstract. A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z 2 -lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by-product, some fundamental representations of affine Kac-Moody Lie algebra of type A (2) n are recovered by the new method.

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