Gelfand-Zetlin basis, Whittaker Vectors and a Bosonic Formula for the Principal Subspace
Boris Feigin
Independent University of Moscow, Russian FederationMichio Jimbo
Rikkyo University, Tokyo, JapanTetsuji Miwa
Kyoto University, Japan

Abstract
We derive a bosonic formula for the character of the principal space in the level vacuum module for , starting from a known fermionic formula for it. In our previous work, the latter was written as a sum consisting of Shapovalov scalar products of the Whittaker vectors for . In this paper we compute these scalar products in the bosonic form, using the decomposition of the Whittaker vectors in the Gelfand-Zetlin basis. We show further that the bosonic formula obtained in this way is the quasi-classical decomposition of the fermionic formula. %for % modules computing it %by using the decomposition %of the Whittaker vectors in the Gelfand-Zetlin basis. %We show that the bosonic formula obtained in this way %is the quasi-classical decomposition of the fermionic formula.
Cite this article
Boris Feigin, Michio Jimbo, Tetsuji Miwa, Gelfand-Zetlin basis, Whittaker Vectors and a Bosonic Formula for the Principal Subspace. Publ. Res. Inst. Math. Sci. 47 (2011), no. 2, pp. 535–551
DOI 10.2977/PRIMS/42