In 1987 Drinfeld [Dr2] gave an extremely important realization of quantum affine algebras [Dr1][Jb]. This new realization has lead to numerous applications such as the vertex representations [FJ][J].… (More)

We introduce an affinization of the quantum KacMoody algebra associated to a symmetric generalized Cartan matrix. Based on the affinization, we construct a representation of the quantum Kac-Moody… (More)

Recent interests in quantum groups are stimulated by their marvelous relations with quantum Yang-Baxter equations, conformal field theory, invariants of links and knots, and q-hypergeometric series.… (More)

As one of the most striking features of quantum phenomena [1], quantum entanglement has been identified as a non-local resource for quantum information processing such as quantum computation [2, 3],… (More)

Based on the shifted Schensted correspondence and the shifted Knuth equivalence, a shifted analog of the Poirier-Reutenauer algebra as a higher lift of Schur’s P-functions and a right coideal… (More)

where the first factor is a symmetric algebra and the second one is a group algebra. The affine algebra ĝ contains a Heisenberg algebra ĥ. One can define the so-called vertex operators X(α, z)… (More)

We establish a q-analog of our recent work on vertex representations and the McKay correspondence. For each finite group Γ we construct a Fock space and associated vertex operators in terms of wreath… (More)

We construct explicitly the q-vertex operators (intertwining operators) for the level one modules V (Λi) of the classical quantum affine algebras of twisted types using interacting bosons, where i =… (More)

Using vertex operators, we construct explicitly Lusztig’s Z[q, q−1]-lattice for the level one irreducible representations of quantum affine algebras of ADE type. We then realize the level one… (More)