Rho-check for LSL2 / LPGL2? « Tom’s Math Weblog

Rho-check for LSL2 / LPGL2?

By trdunlap2

In Kamnitzer we consider the cell $S_w^\mu$ $=\{L:\lim_{s\rightarrow\infty} L\cdot (w\cdot \check\rho)(s)=t^\mu\}$ .

For $SL_2$ , $w\in\{1,-1\}$ permutes the diagonal entries of $\check\rho=\left(\begin{array}{cc} s & 0 \\ 0 & s^{-1}\end{array}\right)$ . When applied to L this will favor one column over another and in the limit will transform L’s tower into a the non-leaning tower with sillouette $\mu$ .

For $LSL_2$ , $w\in\{1,-1\}\times \mathbb{Z}$ but what is $\check\rho$ ?

This entry was posted on September 23, 2008 at 9:53 pm and is filed under Current, Open, Questions. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

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Rho-check for LSL2 / LPGL2?

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