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Arnold Mathematical Journal

, Volume 5, Issue 2–3, pp 373–385 | Cite as

0-Cycles on Grassmannians as Representations of Projective Groups

  • R. Bezrukavnikov
  • M. RovinskyEmail author
Research Contribution
  • 13 Downloads

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.

Notes

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.

References

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Copyright information

© Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019

Authors and Affiliations

  1. 1.MITCambridgeUSA
  2. 2.AG LaboratoryHSE UniversityMoscowRussia
  3. 3.Institute for Information Transmission Problems of Russian Academy of SciencesMoscowRussia

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