M ay 2 00 8 Drinfeld second realization of the quantum affine superalgebras of D ( 1 ) ( 2 , 1 ; x ) via the Weyl groupoid
نویسندگان
چکیده
We obtain Drinfeld second realization of the quantum affine superalgebras associated with the affine Lie superalgebra D(1)(2, 1;x). Our results are analogous to those obtained by Beck for the quantum affine algebras. Beck’s analysis uses heavily the (extended) affine Weyl groups of the affine Lie algebras. In our approach the structures are based on a Weyl groupoid. Preprint numbers: MIT-CTP 3835, HU-EP-07/15
منابع مشابه
On Super RS Algebra and Drinfeld Realization of Quantum Affine Superalgebras
We describe the realization of the super Reshetikhin-Semenov-Tian-Shansky (RS) algebra in quantum affine superalgebras, thus generalizing the approach of Frenkel-Reshetikhin to the supersymmetric (and twisted) case. The algebraic homomorphism between the super RS algebra and the Drinfeld current realization of quantum affine superalgebras is established by using the Gauss decomposition techniqu...
متن کاملA Remark On the FRTS realization and Drinfeld Realization of Quantum Affine Superalgebra
In this paper, we present the hidden symmetry behind the Faddeev-Reshetikhin-TakhtajanSemenov-Tian-Shansky realization of quantum affine superalgebras Uq( ˆ osp(1, 2)) and add the q-Serre relation to the Drinfeld realization of Uq( ˆ osp(1, 2)) [8] derived from the FRTS realization. Mathematics Subject Classifications (1991): 81R10, 17B37
متن کاملar X iv : m at h - ph / 0 70 10 41 v 2 1 9 A pr 2 00 7 Coupled Painlevé VI system with E ( 1 ) 6 - symmetry
We present an new system of ordinary differential equations with affine Weyl group symmetry of type E (1) 6 . This system is expressed as a Hamiltonian system of sixth order with a coupled Painlevé VI Hamiltonian. Introduction The Painlevé equations PJ (J = I, . . . ,VI) are ordinary differential equations of second order. It is known that these PJ admit the following affine Weyl group symmetri...
متن کاملIwahori - Hecke type algebras associated with the Lie superalgebras A ( m , n ) , B ( m , n ) , C ( n ) and D ( m , n ) Hiroyuki Yamane
In this paper we give Iwahori-Hecke type algebras Hq(g) associated with the Lie superalgebras g = A(m,n), B(m,n), C(n) and D(m,n). We classify the irreducible representations of Hq(g) for generic q. Introduction Recently, motivated by a question posed by V. Serganova [S] and study of the Weyl groupoids [H1][H2] associated with Nichols algebras [AS1][AS2] including generalizations of quantum gro...
متن کامل7 Symmetries in the System of Type D ( 1 ) 4 Yusuke Sasano
X iv :0 70 4. 23 31 v1 [ m at h. A G ] 1 8 A pr 2 00 7 SYMMETRIES IN THE SYSTEM OF TYPE D (1) 4 YUSUKE SASANO Abstract. In this paper, we propose a 4-parameter family of coupled Painlevé III systems in dimension four with affine Weyl group symmetry of type D (1) 4 . We also propose its symmetric form in which the D (1) 4 -symmetries become clearly visible. 0. Statement of main results In [9, 10...
متن کامل