HeckeT

The basis element of the Iwahori–Hecke algebra , indexed by a permutation in one-line notation. Multiplication is the -deformation of the symmetric group's.

WikipediaIwahori–Hecke algebra↗WikidataQ1012612↗nLabIwahori–Hecke algebra↗

HeckeT([2,1,3]) for the permutation

Domain: Hecke algebras

Details

• when the length goes up, and when it goes down — the second case is the entire deformation
• So a product of two basis elements is a LINEAR COMBINATION, unlike the other algebra families here; sums read back in, so products compose
• The quadratic relation is , i.e. , replacing
• The braid relations survive the deformation, which is why is the product over ANY reduced word for
• Coefficients stay exact polynomials in ; use HeckeSpecialize to pick a value
• Use the ordered product (NonCommutativeMultiply or ) — is not commutative

Examples

See also: HeckeSpecialize, NonCommutativeMultiply, Basis