Elliptic Ding–Iohara Algebra and the Free Field Realization of the Elliptic Macdonald Operator
نویسندگان
چکیده
منابع مشابه
Commutative Families of the Elliptic Macdonald Operator
In the paper [J. Math. Phys. 50 (2009), 095215, 42 pages], Feigin, Hashizume, Hoshino, Shiraishi, and Yanagida constructed two families of commuting operators which contain the Macdonald operator (commutative families of the Macdonald operator). They used the Ding–Iohara–Miki algebra and the trigonometric Feigin–Odesskii algebra. In the previous paper [arXiv:1301.4912], the present author const...
متن کاملDrinfeld realization of the elliptic Hall algebra
We give a new presentation of the Drinfeld double E of the (spherical) elliptic Hall algebra E+ introduced in our previous work (Burban and Schiffmann in Duke Math. J. preprint math.AG/0505148, 2005). This presentation is similar in spirit to Drinfeld’s ‘new realization’ of quantum affine algebras. This answers, in the case of elliptic curves, a question of Kapranov concerning functional relati...
متن کاملAsymptotic distribution of eigenvalues of the elliptic operator system
Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.
متن کاملModular Transformations of the Elliptic Hypergeometric Functions, Macdonald Polynomials, and the Shift Operator
We consider the space of elliptic hypergeometric functions of the sl2 type associated with elliptic curves with one marked point. This space represents conformal blocks in the sl2 WZW model of CFT. The modular group acts on this space. We give formulas for the matrices of the action in terms of values at roots of unity of Macdonald polynomials of the sl2 type. ⋆ Departement Mathematik, ETH-Zent...
متن کاملThe elliptic algebra Uq,p( ̂ slN ) and the Drinfeld realization of the elliptic quantum group Bq,λ( ̂ slN
By using the elliptic analogue of the Drinfeld currents in the elliptic algebra Uq,p(ŝlN ), we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic quantum group Bq,λ(ŝlN ). For this purpose, we introduce a set of new currents Kj(v) (1 ≤ j ≤ N) in Uq,p(ŝlN ). As in the N = 2 case, we find a structure of Uq,p(ŝlN ) as a certain tensor product of Bq,λ(ŝl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Publications of the Research Institute for Mathematical Sciences
سال: 2014
ISSN: 0034-5318
DOI: 10.4171/prims/139