A (q,γ) analog of the W1+∞ algebra

By K. Miki. 2007

213 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7536ad3297570ea5d90982d8ced19ddb8e829c41

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Citations in the corpus

Representations of quantum toroidal gln (2012, background): “l and relatively easy to handle. We denote En the algebra which is a quotient of Ec n by the relation q c = 1. In this paper we study E n lowest weight modules with rational lowest weights. Following [M], we call such representations quasi-ﬁnite. A quasi-ﬁnite representation has level given by the v”
Quantum Groups and Quantum Cohomology (2012, methodology): “um intermediate long-wave equation is explored in [87]. 1.5.5 In the literature, one can ﬁnd many diﬀerent ways to construct and study algebras that may be called a Yangian of gl[(1), see for example [25, 27, 37, 32, 62, 72, 98, 99]. Perhaps one of the advantages of our approach is that our Y(gl[(1)”
Quantum Geometry and Quiver Gauge Theories (2013, methodology): “In this way, the simplest, gl1 d = 2 toroidal algebra, U aff q ( ĝl1), with quantization parameter q and non-commutativity parameter μ was constructed and studied by Miki in [158] (this gl1-toroidal algebra is called there Uq,γ with the parameter γ related to our μ, cf.”
THE HOMFLYPT SKEIN ALGEBRA OF THE TORUS AND THE ELLIPTIC HALL ALGEBRA (2014, unknown): “ralized quantum aﬃne algebra in [DI97], 1By ‘cousin’ we mean either the ‘positive half’ E+ q,t or a central extension of E q,t. 4 HUGHMORTONANDPETERSAMUELSON • ‘a (q,γ) analog of the W1+∞ algebra’ in [Mik07] • the ‘shuﬄe algebra’ of [FT11], • the ‘spherical gl∞ double aﬃne Hecke algebra’ in [SV11], ”