#20489: A and B bases for Iwahori-Hecke algebras
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Reporter: andrew.mathas | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-7.2
Component: combinatorics | Resolution:
Keywords: Iwahori-Hecke | Merged in:
algebfra | Reviewers:
Authors: Andrew Mathas | Work issues:
Report Upstream: N/A | Commit:
Branch: | 21b4caed9caeb5619f28faf54c3632015fac32a7
u/andrew.mathas/TwoIwahoriHeckeBases| Stopgaps:
Dependencies: |
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Changes (by {'newvalue': u'Andrew Mathas', 'oldvalue': ''}):
* keywords: => Iwahori-Hecke algebfra
* commit: => 21b4caed9caeb5619f28faf54c3632015fac32a7
* author: => Andrew Mathas
Old description:
New description:
This patch implements the A and B bases for the Iwahori-Hecke algebras.
Every Iwahori-Hecke algebra has a unique algebra automorphism `#`, that
Iwahori attributed to Goldman, that sends `T_s` to
`-T_s+q_1+q_2=-(q_1q_2)^{-1}T_s^{-1}`. The A and B bases are invariant
under this involution, up to sign. If `w` belongs to the underlying
Coxeter group then
`A_w = T_w + (-1)^{\ell(w)}T_w^\#`. The element `B_w` is uniquely
determined by the property that
{{{
B_w^\3 = (-1)^{\ell(w)}B_w
B_w = T_w+\sum_{v<w, \ell(v)\not\equiv\ell(w)\pmod 2} b_{vw}(q)T_v.
}}}
This ticket implements both of these bases, together with the Goldman
involution.
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Ticket URL: <http://trac.sagemath.org/ticket/20489#comment:3>
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