Summary
In tikya[GK] we developed a framework to study representations of groups of the form G((t)), where G is an algebraic group over a local field K. The main feature of this theory is that natural representations of groups of this kind are not on vector spaces, but rather on pro-vector spaces.
In this paper we present some further constructions related to this theory. The main results include: 1) General theorems insuring representability of covariant functors, 2) Study of the functor of semi-invariants, which is an analog of the functor of semi-infinite cohomology for infinite-dimensional Lie algebras, 3) Construction of representations from the moduli space of G-bundles on algebraic curve over K.
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References
D. Gaitsgory, D. Kazhdan, Representations of algebraic groups over a 2-dimensional local field, math.RT/0302174, GAFA 14 (2004), 535–574.
M. Kapranov, Double affine Hecke algebras and 2-dimensional local fields, JAMS 14 (2001), 239–262.
M. Kapranov, The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups, math.AG/0001005.
Positselsky, Private communications.
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Dedicated to A. Joseph on his 60th birthday
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© 2006 Birkhäuser Boston
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Gaitsgory, D., Kazhdan, D. (2006). Algebraic groups over a 2-dimensional local field: Some further constructions. In: Bernstein, J., Hinich, V., Melnikov, A. (eds) Studies in Lie Theory. Progress in Mathematics, vol 243. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4478-4_7
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DOI: https://doi.org/10.1007/0-8176-4478-4_7
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4342-3
Online ISBN: 978-0-8176-4478-9
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