Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Representations of the Kauffman bracket skein algebra of the punctured torus

100%

Cho J.-P., Gelca R.

Fundamenta Mathematicae

2014

tom 225

nr 1

45-55

We describe the action of the Kauffman bracket skein algebra on some vector spaces that arise as relative Kauffman bracket skein modules of tangles in the punctured torus. We show how this action determines the Reshetikhin-Turaev representation of the punctured torus. We rephrase our results to describe the quantum group quantization of the moduli space of flat SU(2)-connections on the punctured torus with fixed trace of the holonomy around the boundary.

Quantum mechanics and nonabelian theta functions for the gauge group SU(2)

100%

Gelca R., Uribe A.

Fundamenta Mathematicae

2015

tom 228

nr 2

97-137

We propose a direction of study of nonabelian theta functions by establishing an analogy between the Weyl quantization of a one-dimensional particle and the metaplectic representation on the one hand, and the quantization of the moduli space of flat connections on a surface and the representation of the mapping class group on the space of nonabelian theta functions on the other. We exemplify this with the cases of classical theta functions and of the nonabelian theta functions for the gauge group SU(2). The emphasis of the paper is on this analogy and on the possibility of generalizing this approach to other gauge groups, and not on the results, of which some have appeared elsewhere.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Gelca R.

1 Cho J.-P.

1 Uribe A.

1 2015

1 2014

Wyniki wyszukiwania

Representations of the Kauffman bracket skein algebra of the punctured torus

Quantum mechanics and nonabelian theta functions for the gauge group SU(2)