Free field realizations of the Date-Jimbo-Kashiwara-Miwa algebra

We use the description of the universal central extension of the DJKM algebra $\mathfrak{sl}(2, R)$ where $R=\mathbb C[t,t^{-1},u\,|\,u^2=t^4-2ct^2+1 ]$ given in earlier work to construct realizations of the DJKM algebra in terms of sums of partial differential operators.Comment: arXiv admin note: substantial text overlap with arXiv:1303.697

Free Field Representation of Quantum Affine Algebra U_q(\hat{sl}_2)

A Fock representation of the quantum affine algebra U_q(\widehat{\sl}_2) is constructed by three bosonic fields for an arbitrary level with the help of the Drinfeld realization.Comment: 11 page