Quantum groups, quantum tori, and the Grothendieck–Springer resolution

Gus Schrader*, Alexander Shapiro

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We construct an algebra embedding of the quantum group Uq(g) into a central extension of the quantum coordinate ring Oq[Gw0,w0 /H] of the reduced big double Bruhat cell in G. This embedding factors through the Heisenberg double Hq of the quantum Borel subalgebra U≥0, which we relate to Oq[G] via twisting by the longest element of the quantum Weyl group. Our construction is inspired by the Poisson geometry of the Grothendieck–Springer resolution studied in [10], and the quantum Beilinson–Bernstein theorem investigated in [2] and [36].

Original languageEnglish (US)
Pages (from-to)431-474
Number of pages44
JournalAdvances in Mathematics
StatePublished - Dec 1 2017
Externally publishedYes


  • Grothendieck–Springer resolution
  • Hopf algebras
  • Quantum groups

ASJC Scopus subject areas

  • General Mathematics


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