4 problems

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The archimedean Ramanujan–Selberg conjecture for cusp forms on $SL_3(\mathbb{Z})$
A cusp form on $SL_3(\mathbb{Z})\backslash \mathcal{H}$ has Langlands parameters $\{\ell_1,\ell_2,\ell_3\}$ satisfying $\ell_1+\ell_2+\ell_3=0$ . It is tempered when each…
Conjectureopenautomorphic-forms sl3 temperednessarXiv posted 2 days ago
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Arborization conjecture for tagged non-elliptic SL3 webs
Let $\mathcal{M}$ be one of the moduli spaces considered in the paper, and let $[(T,varphi)]inmathscr{A}(\mathcal{M})$ be a tagged non-elliptic ${\rm SL}_3$ web invariant. The arbo…
Conjectureopencluster-algebras sl3 web-diagramsarXiv posted 2 days ago
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Lusztig–Williamson's billiards conjecture for second-generation tilting characters of ${\rm SL}_3$
Let $G={\rm SL}_3$ , and let $d_{y,x}^{2,1}$ denote the coefficients governing the second-generation tilting characters, with their $v$ -analogues defined through the $p$ -canonical b…
Conjectureopenrepresentation-theory sl3 tilting-modulesarXiv posted 2 days ago
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Khovanov–Rozansky's equivalence conjecture for rational $sl_3$ link homologies
Let the universal rational $sl_n$ link homology theory constructed by Khovanov and Rozansky be given for $n>0$ , and let the universal integer $sl_3$ link homology constructed using…
Conjectureopenlink-homology matrix-factorizations sl3arXiv posted 2 days ago

The archimedean Ramanujan–Selberg conjecture for cusp forms on SL3(Z)SL_3(\mathbb{Z})SL3​(Z)