Elliptic Quantum Group U_q,p(B_N⁽¹⁾) and Vertex Operators

2014/07/14 by Hitoshi Konno, Konno, Hitoshi, Kazuyuki Oshima +1
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.1407.3601

53 pages

arxiv created 2014/07/14 · arxiv updated 2014/07/15

Abstract

Assuming the existence of the L-operators, we study the Hopf algebroid structure of U_q,p(B_N⁽¹⁾). As an application, we derive the type I and II vertex operators, which intertwine the U_q,p(B_N⁽¹⁾)-modules of generic level, by assuming some analytic properties of the L-operators. For the level-1 case, we construct their free field realizations and show that the results satisfy the desired commutation relations with coefficients given by the elliptic dynamical R-matrices of the B_N⁽¹⁾ type.

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