相关论文: Difference L operators related to q-characters
We propose factorized difference operators L(u) associated with the twisted quantum affine algebras U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}), U_{q}(D^{(2)}_{n+1}),U_{q}(D^{(3)}_{4}). These operators are shown to be annihilated by a…
Frenkel-Reshetikhin introduced $q$-characters of finite dimensional representations of quantum affine algebras. We give a combinatorial algorithm to compute them for all simple modules. Our tool is $t$-analogue of the $q$-characters, which…
A unified and systematic scheme for constraction of differential opreator realization of any irreducible representation of $sl(n)$ is developed. The $q$-analogue of this unified scheme is used to constract $q$-difference operator…
Let $(\mathbf{U}, \mathbf{U}^\imath)$ be a split affine quantum symmetric pair of type $\mathsf{B}_n^{(1)}, \mathsf{C}_n^{(1)}$ or $\mathsf{D}_n^{(1)}$. We prove factorization and coproduct formulae for the Drinfeld-Cartan operators…
Frenkel and Reshetikhin introduced screening operators related to q-characters of finite dimensional representations of quantum affine algebras. We propose t-analogs of screening operators related to Nakajima's q,t-characters with the same…
We construct representations $\hat\pi_{\br}$ of the quantum algebra $U_q(sl(n))$ labelled by $n-1$ complex numbers $r_i$ and acting in the space of formal power series of $n(n-1)/2$ non-commuting variables. These variables generate a flag…
We show that the quantum affine algebra U_{q}(A_{1}^{(1)}) and the quantum affine superalgebra U_{q}(C(2)^{(2)}) admit unified description. The difference between them consists in the phase factor which is equal to 1 for U_{q}(A_{1}^{(1)})…
Utilizing the multiplicative formula of universal R matrix, the correspondence between the L operators and Drinfeld's generators is explicitly calculated for quantum group U_q(g) with g=A_l^{(1)}, B_l^{(1)}, C_l^{(1)}, D_l^{(1)}.
Integral representations of two $q$-difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to $q$-difference equations in the complex domain. Both representations are unified through…
A representation of the quantum superalgebra Uq(sl(M+1|N+1)) is constructed based on the q-differential operators acting on the coherent states parameterized by coordinates. These coordinates correspond to the local ones of the flag…
We analyze the properties of the q-vertex operators of U_q(sl(2)^) introduced by Frenkel and Reshetikhin. As the condition for the null vector decoupling, we derive the existence condition of the q-vertex operators ( the fusion rules ).
There are several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative related…
The structure positive of unitary irreducible representations of the noncompact $u_q(2,1)$ quantum algebra that are related to a positive discrete series is examined. With the aid of projection operators for the $su_q(2)$ subalgebra, a…
We investigate the characters of some finite-dimensional representations of the quantum affine algebras $U_q(\hat{g})$ using the action of the copy of $U_q(g)$ embedded in it. First, we present an efficient algorithm for computing the…
We give a supersymmetric generalization of the sine algebra and the quantum algebra $U_{t}(sl(2))$. Making use of the $q$-pseudo-differential operators graded with a fermionic algebra, we obtain a supersymmetric extension of sine algebra.…
We prove the Kirillov-Reshetikhin conjecture concerning certain finite dimensional representations of a quantum affine algebra $\Ua$ when $\hat\g$ is an untwisted affine Lie algebra of type $ADE$. We use $t$--analog of $q$--characters…
The q-character is a strong tool to study finite-dimensional representations of quantum affine algebras. However, the explicit formula of the q-character of a given representation has not been known so far. Frenkel and Mukhin proposed the…
Some relations between different objects associated with quantum affine algebras are reviewed. It is shown that the Frenkel-Jing bosonization of a new realization of quantum affine algebra $\Uqa$ as well as bosonization of $L$-operators for…
We introduce a new set of $q$-difference operators acting as raising operators on a family of symmetric polynomials which are characters of graded tensor products of current algebra ${\mathfrak g}[u]$ KR-modules \cite{FL} for ${\mathfrak…
We study linear recurrence relations in the character solutions of $Q$-systems obtained from the Kirillov-Reshetikhin modules. We explain how known results on difference $L$-operators lead to a uniform construction of linear recurrences in…