Shifted quantum affine algebras: integral forms in type $A$ (with appendices by Alexander Tsymbaliuk and Alex Weekes)
| Autor: | Finkelberg, Michael, Tsymbaliuk, Alexander |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Arnold Mathematical Journal 5 (2019), no. 2, 197-283 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s40598-019-00118-7 |
| Popis: | We define an integral form of shifted quantum affine algebras of type $A$ and construct Poincar\'e-Birkhoff-Witt-Drinfeld bases for them. When the shift is trivial, our integral form coincides with the RTT integral form. We prove that these integral forms are closed with respect to the coproduct and shift homomorphisms. We prove that the homomorphism from our integral form to the corresponding quantized $K$-theoretic Coulomb branch of a quiver gauge theory is always surjective. In one particular case we identify this Coulomb branch with the extended quantum universal enveloping algebra of type $A$. Finally, we obtain the rational (homological) analogues of the above results (proved earlier in arXiv:1611.06775, arXiv:1806.07519 via different techniques). Comment: v1: 65 pages. v2: 67 pages; added a dominance condition in Section 2(vii), another definition in Appendix A(viii), the injectivity of $\mathfrak{g}\to Y$ in Appendix B(ii). v3: 70 pages; table of contents added, Section 3(vi) updated and Remark 4.33 added. v4: 70 pages; this is a slight modification of the version published in the Arnold Mathematical Journal, the difference is in the introduction |
| Databáze: | arXiv |
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