4 problems

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Positivity conjecture for KL-Schubert class localizations
KL-Schubert positivity conjecture. The evaluation $({\mathfrak S}_v)_w$ , for any $w\leq v$ , can be expressed as a possibly infinite sum of monomials in the $y_{-\alpha}$ , where…
Conjecturesolvedequivariant-elliptic-cohomology positivity schubert-calculusarXiv posted 2 days ago
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Geometric realization conjecture for the level-(0,-1) representation
Let ${\mathcal U}$ be the elliptic quantum toroidal algebra considered in the paper, and let ${\mathcal F}^{(0,-1)}_u$ be the level-(0,-1) representation on the vector space with b…
Conjectureopenelliptic-quantum-groups equivariant-elliptic-cohomology hilbert-schemesarXiv posted 2 days ago
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KL-Schubert classes coincide with Bott–Samelson classes for smooth Schubert varieties
Smooth-case coincidence conjecture. The KL-Schubert classes coincide with the corresponding smooth-case classes.
Conjectureopenequivariant-elliptic-cohomology flag-varieties schubert-calculusarXiv posted 2 days ago
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The representation-theoretic role of equivariant elliptic cohomology for loop groups
Loop-group elliptic cohomology conjecture. Equivariant elliptic cohomology $\mathcal E ll_G$ should play the same role for the representation theory of ${\mathcal L G}$ that $K_G$ …
Conjectureopenequivariant-elliptic-cohomology loop-groups representation-theoryarXiv posted 2 days ago

Positivity conjecture for KL-Schubert class localizations