Duality theorems for current groups

Evgeny Feigin, Anton Khoroshkin, Ievgen Makedonskyi

Research output: Contribution to journalArticlepeer-review


The classical Peter—Weyl theorem describes the structure of the space of functions on a semi-simple algebraic group. On the level of characters (in type A) this boils down to the Cauchy identity for the products of Schur polynomials. We formulate and prove an analogue of the Peter—Weyl theorem for current groups. In particular, in type A the corresponding characters identity is governed by the Cauchy identity for the products of q-Whittaker functions. We also formulate and prove a version of the Schur—Weyl theorem for current groups, which can be seen as a specialization of a theorem due to Drinfeld and Chari—Pressley. The link between the Peter—Weyl and Schur—Weyl theorems is provided by the (current version of) Howe duality.

Original languageEnglish
Pages (from-to)441-479
Number of pages39
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - May 2022
Externally publishedYes

Bibliographical note

Funding Information:
We are grateful to Alexei Borodin, Alexander Braverman, Boris Feigin, Michael Finkelberg, Ryo Fujita, Syu Kato and Shrawan Kumar for useful discussions and correspondence. The research of E. F. was supported by the grant RSF 19-11-00056. The study was partially supported by the HSE University Basic Research Program. A. Kh. is a Young Russian Mathematics award winner and would like to thank its sponsors and jury. The work of Ie. M. was supported by the Japan Society for the Promotion of Science.

Publisher Copyright:
© 2022, The Hebrew University of Jerusalem.

ASJC Scopus subject areas

  • Mathematics (all)


Dive into the research topics of 'Duality theorems for current groups'. Together they form a unique fingerprint.

Cite this