Fock Space Representation of the Circle Quantum Group

In [12] we have defined quantum groups U-upsilon(sl(R)) and U-upsilon(sl(S-1)), which can be interpreted as continuum generalizations of the quantum groups of the Kac-Moody Lie algebras of finite, respectively affine type A. In the present paper, we define the Fock space representation F-R of the quantum group U-upsilon(sl(R)) as the vector space generated by real pyramids (a continuum generalization of the notion of partition). In addition, by using a variant version of the "folding procedure" of Hayashi-Misra-Miwa, we define an action of U-upsilon(sl(S-1)) on F-R.