Hecke-Clifford algebras and spin Hecke algebras III: the trigonometric type
Ta Khongsap
TL;DR
This paper introduces and studies trigonometric spin double affine Hecke algebras and Hecke-Clifford algebras, establishing their foundational properties and an isomorphism between them, advancing the algebraic understanding of these structures.
Contribution
It defines new algebraic structures (tsDaHa and tDaHCa), proves the PBW basis property, and establishes an isomorphism between these algebras, extending the theory of Hecke algebras.
Findings
PBW basis property established for tDaHCa and tsDaHa
An algebra isomorphism between tDaHCa and tsDaHa
Introduction of trigonometric spin double affine Hecke algebras
Abstract
The notion of trigonometric spin double affine Hecke algebras (tsDaHa) and trigonometric double affine Hecke-Clifford algebras (tDaHCa) associated to classical Weyl groups are introduced. The PBW basis property is established. An algebra isomorphism relating tDaHCa to tsDaHa is obtained.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra