Inhomogeneous lattice paths are introduced as ordered sequences of rectangular Young tableaux thereby generalizing recent work on the Kostka polynomials by Nakayashiki and Yamada and by Lascoux,… (More)

Using new q-functions recently introduced by Hatayama et al. and by (two of) the authors, we obtain an A2 version of the classical Bailey lemma. We apply our result, which is distinct from the A2… (More)

We define a bijection from Littlewood–Richardson tableaux to rigged configurations and show that it preserves the appropriate statistics. This proves in particular a quasi-particle expression for the… (More)

We present and prove Rogers–Schur–Ramanujan (Bose/Fermi) type identities for the Virasoro characters of the minimal model M(p, p). The proof uses the continued fraction decomposition of p/p… (More)

We introduce " virtual " crystals of the affine types g = D (2) n+1 , A (2) 2n and C (1) n by naturally extending embeddings of crystals of types Bn and Cn into crystals of type A 2n−1.… (More)

Using the methods of [14] and recent results on the characters of Kirillov–Reshetikhin modules [9, 10, 24], the existence of Kirillov–Reshetikhin crystals B is established for all nonexceptional… (More)

q-Analogues of the coefficients of x in the expansion of ∏N j=1(1 + x + · · · + x )j are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the… (More)

General fermionic expressions for the branching functions of the rational coset conformal field theories ŝu(2)M × ŝu(2)N/ŝu(2)M+N are given. The equality of the bosonic and fermionic representations… (More)

We provide the explicit combinatorial structure of the Kirillov– Reshetikhin crystals B r,s of type D (1) n , B (1) n , and A (2) 2n−1. This is achieved by constructing the crystal analogue σ of the… (More)