Quantum groups in three-dimensional integrability
著者
書誌事項
Quantum groups in three-dimensional integrability
（Theoretical and mathematical physics）
Springer, c2022
- : hbk
大学図書館所蔵 件 / 全11件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 321-327) and index
内容説明・目次
内容説明
Quantum groups have been studied intensively in mathematics and have found many valuable applications in theoretical and mathematical physics since their discovery in the mid-1980s. Roughly speaking, there are two prototype examples of quantum groups, denoted by Uq and Aq. The former is a deformation of the universal enveloping algebra of a Kac-Moody Lie algebra, whereas the latter is a deformation of the coordinate ring of a Lie group. Although they are dual to each other in principle, most of the applications so far are based on Uq, and the main targets are solvable lattice models in 2-dimensions or quantum field theories in 1+1 dimensions. This book aims to present a unique approach to 3-dimensional integrability based on Aq. It starts from the tetrahedron equation, a 3-dimensional analogue of the Yang-Baxter equation, and its solution due to work by Kapranov-Voevodsky (1994). Then, it guides readers to its variety of generalizations, relations to quantum groups, and applications. They include a connection to the Poincare-Birkhoff-Witt basis of a unipotent part of Uq, reductions to the solutions of the Yang-Baxter equation, reflection equation, G2 reflection equation, matrix product constructions of quantum R matrices and reflection K matrices, stationary measures of multi-species simple-exclusion processes, etc. These contents of the book are quite distinct from conventional approaches and will stimulate and enrich the theories of quantum groups and integrable systems.
目次
Introduction.- Tetrahedron equation.- 3D R from quantized coordinate ring of type A.- 3D reflection equation and quantized reflection equation.- 3D K from quantized coordinate ring of type C.- 3D K from quantized coordinate ring of type B.- Intertwiners for quantized coordinate ring Aq (F4).- Intertwiner for quantized coordinate ring Aq (G2).- Comments on tetrahedron-type equation for non-crystallographic Coxeter groups.- Connection to PBW bases of nilpotent subalgebra of Uq.- Trace reductions of RLLL = LLLR.- Boundary vector reductions of RLLL = LLLR.- Trace reductions of RRRR = RRRR.- Boundary vector reductions of RRRR = RRRR.- Boundary vector reductions of (LGLG)K = K(GLGL).- Reductions of quantized G2 reflection equation.- Application to multispecies TASEP.
「Nielsen BookData」 より
