680 research outputs found

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

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    We use the description of the universal central extension of the DJKM algebra sl(2,R)\mathfrak{sl}(2, R) where R=C[t,t1,uu2=t42ct2+1] 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)

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    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