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\(q\)-difference conformal invariant operators and equations. (English) Zbl 0907.17019
Slovák, Jan (ed.), Proceedings of the 15th Winter School on geometry and physics, Srní, Czech Republic, January 14–21, 1995. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43, 15-55 (1996).
This paper is a survey of the author’s work. Section 1 is devoted to a summary of the classical case. Section 2 and part of Section 3 review part of the exposition of V. K. Dobrev, [J. Phys. A 27, 4841-4857 (1994; Zbl 0843.17016); Note added 6633-6634 (1994; Zbl 0895.17006)] for \(U_q(sl(n))\) with general \(n\). Then in Sections 4 and 5, he considers in detail the case \(n=4\) following part of the exposition of [\(q\)-difference intertwining operators for \(U_q(sl(4))\) and \(q\)-conformal invariant equations (to appear)]. In Section 6, following mostly [New \(q\)-Minkowski space-time and \(q\)-Maxwell equations hierarchy from \(q\)-conformal invariance, Phys. Lett. B 341, 133-138 (1994), Corrigendum B 346, 427 (1995) and Representations of quantum groups and \(q\)-deformed invariant wave equations, Habilitation Thesis, Clausthal (1994)], he uses \(q\)-conformal invariance to propose new \(q\)-Minkowski space-time and \(q\)-Maxwell hierarchy equations.
For the entire collection see [Zbl 0884.00042].
17B37 Quantum groups (quantized enveloping algebras) and related deformations
39A70 Difference operators
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory