%0 Journal Article
%T Quantum Algebraic Approach to Refined Topological Vertex
%A H. Awata
%A B. Feigin
%A J. Shiraishi
%J Mathematics
%D 2011
%I arXiv
%R 10.1007/JHEP03(2012)041
%X We establish the equivalence between the refined topological vertex of Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W_{1+infty} introduced by Miki. Our construction involves trivalent intertwining operators Phi and Phi^* associated with triples of the bosonic Fock modules. Resembling the topological vertex, a triple of vectors in Z^2 is attached to each intertwining operator, which satisfy the Calabi-Yau and smoothness conditions. It is shown that certain matrix elements of Phi and Phi^* give the refined topological vertex C_{lambda mu nu}(t,q) of Iqbal-Kozcaz-Vafa. With another choice of basis, we recover the refined topological vertex C_{lambda mu}^nu(q,t) of Awata-Kanno. The gluing factors appears correctly when we consider any compositions of Phi and Phi^*. The spectral parameters attached to Fock spaces play the role of the K"ahler parameters.
%U http://arxiv.org/abs/1112.6074v1