Double Yangians and lattice quantum vertex algebras

2025/09/20 by Kong, Fei, Li, Haisheng
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2509.16592

Abstract

For any simply-laced GCM A, a \mathbb C[[ℏ]]-algebra \widehatDY(A) was introduced in [KL1], where it was proved that the universal vacuum \widehatDY(A)-module V_A(ℓ) for any fixed level ℓ is naturally an ℏ-adic weak quantum vertex algebra. Let L be the root lattice of \mathfrak g(A). As the main results of this paper, we construct an ℏ-adic quantum vertex algebra V_L[[ℏ]]^η as a formal deformation of the lattice vertex algebra V_L and show that every V_L[[ℏ]]^η-module is naturally a restricted \widehatDY(A)-module of level one. For A of finite type, we obtain a realization of V_L[[ℏ]]^η as a quotient of the ℏ-adic weak quantum vertex algebra V_A(1), giving a characterization of V_L[[ℏ]]^η-modules as restricted \widehatDY(A)-modules of level one.

Citations

• Double Yangians and quantum vertex algebras, I
• On vertex algebras and their modules associated with even lattices
• A smash product construction of nonlocal vertex algebras
• Axiomatic G₁-vertex algebras
• Simple vertex operator algebras are nondegenerate
• Central Extension of the Yangian Double

Related

• Double Yangians and quantum vertex algebras, I
• ℏ-adic quantum vertex algebras and their modules
• Quantum vertex algebra associated to quantum toroidal \mathfrakgl_N
• Quantum vertex F((t))-algebras and their modules
• Ding-Iohara algebras and quantum vertex algebras