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Positivity of Iwahori–Hecke algebra characters on the Kazhdan-Lusztig basis

Finally, most of the positivity properties in the Hecke algebras can be proven using the categorification with Soergel bimodules. Is there a categorification of the irreducible characters? …
AThomas's user avatar
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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 …
AThomas's user avatar
  • 617
3 votes

Positivity of Iwahori–Hecke algebra characters on the Kazhdan-Lusztig basis

The second question is easy to answer: I certainly have never seen any reference discussing/calculating how the simple characters of KL basis elements look like - left aside positivity or positive integral …