Timeline for On $p$-adic Iwahori-spherical Whittaker functions
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 17, 2023 at 12:51 | comment | added | Maty Mangoo | I think it is better if you leave the answer. I now added a little more to my already overloaded content by trying to explain in more detail what I wish to obtain. | |
| Apr 15, 2023 at 23:14 | comment | added | David Loeffler | I see. So it looks like you were actually asking a different and more subtle question from the one I answered – apologies for jumping to conclusions! Do you want me to delete this answer? That might increase the chances of a real expert coming along and answering your actual question. | |
| Apr 15, 2023 at 18:13 | comment | added | Maty Mangoo | Bump and co. calls this operator in the recursion a modified Kazdhan-Lusztig operator. What I would be interested in is understand this transition by means of rep.theory. | |
| Apr 15, 2023 at 18:09 | comment | added | Maty Mangoo | while it is true that (at least for the long Weyl-element), the (Iwahori-spherical) Whittaker function restricted to the diagonal torus has the form you stated, its values on $\pi^e \cdot w$ are not so easy to describe. In deed, if one sticks to $n=2$, then for example for $w = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$ one gets $$ \mathcal{W}(\pi^e w) = (\delta^{1/2}_2 \otimes \tau^{w})(\pi^{e}) \cdot \left(\frac{1 - q^{-1} + q^{-1}\left(\frac{\alpha}{\beta}\right)^{e_2-e_1 + 2} - \left(\frac{\alpha}{\beta}\right)^{e_2-e_1 + 1}}{1 - \frac{\alpha}{\beta}}\right). $$ | |
| Apr 15, 2023 at 16:48 | history | answered | David Loeffler | CC BY-SA 4.0 |