QuantumMACMAHON, a Maple package that verifies the Quantum Macmahon Master Theorem for any specific dimension. It accompanies the article ”The Quantum MacMahon Master Theorem” by S. Garoufalidis, T. Le and D. Zeilberger: The MacMahon’s Master Theorem relates a certain generating function obtained from a square matrix A and the determinant of I-A. An equivalent formulation of this theorem is the boson-fermion correspondence in physics. In order to formulate the quantum version of the MacMahon’s Master Theorem, the authors considered the quantum determinant of right-quantum (non-commutative) matrices. The formula obtained in this paper relates a certain generating function obtained from a right-quantum matrix A and some linear combination of quantum determinants of sub-matrices of A. This formula recovers the boson-fermion correspondence when the quantum parameter is specialized to 1. The authors were motivated by recent developments in quantum topology.

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Jing, Naihuan; Kožić, Slaven; Molev, Alexander; Yang, Fan: Center of the quantum affine vertex algebra in type $A$ (2018)
  2. Futorny, Vyacheslav; Molev, Alexander: Quantization of the shift of argument subalgebras in type $A$ (2015)
  3. Chervov, A.; Falqui, G.; Rubtsov, V.; Silantyev, A.: Algebraic properties of Manin matrices. II: $q$-analogues and integrable systems (2014)
  4. Calixto, M.; Pérez-Romero, E.: Extended MacMahon-Schwinger’s master theorem and conformal wavelets in complex Minkowski space (2011)
  5. Chervov, A.; Falqui, G.; Rubtsov, V.: Algebraic properties of Manin matrices. I (2009)
  6. Foata, Dominique; Han, Guo-Niu: A basis for the right quantum algebra and the “$1= q$” principle (2008)
  7. Hai, Phùng H^o; Kriegk, Beno^ıt; Lorenz, Martin: $N$-homogeneous superalgebras. (2008)
  8. Foata, Dominique; Han, Guo-Niu: A new proof of the Garoufalidis-L^e-Zeilberger quantum MacMahon master theorem (2007)
  9. Foata, Dominique; Han, Guo-Niu: Specializations and extensions of the quantum MacMahon master theorem (2007)
  10. Huynh, Vu; L^e, Thang T.Q.: On the colored Jones polynomial and the Kashaev invariant (2007)
  11. Konvalinka, Matjaž; Pak, Igor: Non-commutative extensions of the MacMahon Master Theorem (2007)
  12. Lauve, Aaron; Taft, Earl J.: A class of left quantum groups modeled after $\textSL_q(n)$. (2007)
  13. Garoufalidis, Stavros; L^e, Thang T.Q.; Zeilberger, Doron: The quantum MacMahon master theorem (2006)
  14. Garoufalidis, Stavros; Loebl, Martin: A non-commutative formula for the colored Jones function (2006)
  15. Garoufalidis, Stavros; L^e, Thang T.Q.: The colored Jones function is $q$-holonomic (2005)