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Results tagged with hecke-algebras
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user 142627
10
votes
3
answers
409
views
Positivity of Iwahori–Hecke algebra characters on the Kazhdan-Lusztig basis
$\DeclareMathOperator\tr{tr}$I'm interested in the irreducible characters of a finite Iwahori–Hecke algebra evaluated at the Kazhdan–Lusztig basis. These are Laurent polynomials.
Are the coefficients …
- 617
3
votes
Positivity of Iwahori–Hecke algebra characters on the Kazhdan-Lusztig basis
Following the hint of Geordie Williamson, I contacted Daniel Tubbenhauer, one of the authors of the paper on categorification. With his agreement, I put here his answer:
"These are actually very inter …
- 617
3
votes
Positivity of Iwahori–Hecke algebra characters on the Kazhdan-Lusztig basis
I checked using the Chevie package of Gap3. It seems that for all types apart $A_n$, there are negative coefficients in some values of characters on the KL-basis.
The smallest example is type $B_2$. S …
- 617
6
votes
1
answer
203
views
Positivity of Schur elements in Iwahori-Hecke algebras
I'm interested in finite Iwahori-Hecke algebras.
If $\mathcal{H}$ is such a Hecke algebra, defined over $\mathbb{Z}[q^{\pm 1/2}]$, and $\Lambda$ an irreductible representation, there is the notion of …
- 617
2
votes
Positivity of Schur elements in Iwahori-Hecke algebras
Together with Maria Chlouveraki, we determined the answer:
The Schur elements are positive in all classical types $A_n, B_n$ and $D_n$ (use the formula of Theorem 4.3. in https://hal.archives-ouvertes …
- 617