scholarly journals A Laurent Series Proof of the Habsieger-Kadell $q$-Morris Identity

10.37236/4221 ◽  
2014 ◽  
Vol 21 (3) ◽  
Author(s):  
Xin Guoce ◽  
Zhou Yue
Keyword(s):  
Laurent Series ◽  
Constant Term ◽  
Additional Parameter ◽  
Common Generalization ◽  
Constant Term Identity

We give a Laurent series proof of the Habsieger-Kadell $q$-Morris identity, which is a common generalization of the $q$-Morris identity and the Aomoto constant term identity. The proof allows us to extend the theorem for some additional parameter cases.

Quantum Q-Systems and Fermionic Sums—The Non-Simply Laced Case

2020 ◽  
Author(s):  
Mingyan Simon Lin
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence ◽  
Constant Term ◽  
Fusion Product ◽  
Full Generality ◽  
Quantum Cluster ◽  
Constant Term Identity ◽  
Q System ◽  
Explicit Expressions

Abstract In this paper, we seek to prove the equality of the $q$-graded fermionic sums conjectured by Hatayama et al. [ 14] in its full generality, by extending the results of Di Francesco and Kedem [ 9] to the non-simply laced case. To this end, we will derive explicit expressions for the quantum $Q$-system relations, which are quantum cluster mutations that correspond to the classical $Q$-system relations, and write the identity of the $q$-graded fermionic sums as a constant term identity. As an application, we will show that these quantum $Q$-system relations are consistent with the short exact sequence of the Feigin–Loktev fusion product of Kirillov–Reshetikhin modules obtained by Chari and Venkatesh [ 5].

ADE SUBALGEBRAS OF THE TRIPLET VERTEX ALGEBRA 𝒲(p): D-SERIES

2014 ◽  
Vol 25 (01) ◽  
pp. 1450001 ◽  
Author(s):  
DRAŽEN ADAMOVIĆ ◽  
XIANZU LIN ◽  
ANTUN MILAS
Keyword(s):  
Vertex Algebra ◽  
Constant Term ◽  
Independent Interest ◽  
Irreducible Modules ◽  
Constant Term Identity ◽  
General Method

We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra 𝒲(p) initiated in D. Adamović, X. Lin and A. Milas, ADE subalgebras of the triplet vertex algebra 𝒲(p): Am-series, Commun. Contemp. Math.15 (2013), Article ID: 1350028, 1–30. This part deals with the dihedral series. First, subject to a certain constant term identity, we classify all irreducible modules for the vertex algebra [Formula: see text], the ℤ2-orbifold of the singlet vertex algebra [Formula: see text]. Then, we classify irreducible modules and determine Zhu's and C2-algebra for the vertex algebra 𝒲(p)D2. A general method for construction of twisted 𝒲(p)-modules is also introduced. We also discuss classification of twisted [Formula: see text]-modules including the twisted Zhu's algebra [Formula: see text], which is of independent interest. The category of admissible Ψ-twisted [Formula: see text]-modules is expected to be semisimple. We also prove C2-cofiniteness of 𝒲(p)Dm for all m, and give a conjectural list of irreducible 𝒲(p)Dm-modules. Finally, we compute characters of the relevant irreducible modules and describe their modular closure.

Sign in / Sign up

Export Citation Format

Share Document