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0-Cycles on Grassmannians as Representations of Projective Groups

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Abstract

Let F be an infinite division ring, V be a left F-vector space, \(r\ge 1\) be an integer. We study the structure of the representation of the linear group \(\mathrm {GL}_F(V)\) in the vector space of formal finite linear combinations of r-dimensional vector subspaces of V with coefficients in a field. This gives a series of natural examples of irreducible infinite-dimensional representations of projective groups. These representations are non-smooth if F is locally compact and non-discrete.

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Acknowledgements

We are grateful to Leonid Rybnikov and Sasha Kazilo for bringing us together and providing an exceptional enviroment that made our work possible. The study has been funded within the framework of the HSE University Basic Research Program and the Russian Academic Excellence Project ‘5-100’. R.B. is partially supported by an NSF grant.

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Authors and Affiliations

  1. MIT, Office 2-470, 77 Massachusetts Ave, Cambridge, MA, 02139, USA

    R. Bezrukavnikov

  2. AG Laboratory, HSE University, 6 Usacheva Str., Moscow, Russia, 119048

    M. Rovinsky

  3. Institute for Information Transmission Problems of Russian Academy of Sciences, Moscow, Russia

    R. Bezrukavnikov & M. Rovinsky

Authors
  1. R. Bezrukavnikov
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  2. M. Rovinsky
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Correspondence to M. Rovinsky.

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Рафаилу Калмановичу Гордину.

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Bezrukavnikov, R., Rovinsky, M. 0-Cycles on Grassmannians as Representations of Projective Groups. Arnold Math J. 5, 373–385 (2019). https://doi.org/10.1007/s40598-019-00126-7

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  • DOI: https://doi.org/10.1007/s40598-019-00126-7

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