Browsing by Subject "mathematical physics"

Now showing 1 - 3 of 3
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    Branching rules for quantum toroidal gl (n)
    (2013) Feigin, B.; Jimbo, M.; Miwa, T.; Mukhin, Eugene; Department of Mathematical Sciences, School of Science
    We construct an analog of the subalgebra Ugl(n) ⊗ Ugl(m) ⊂ Ugl(m + n) in the setting of quantum toroidal algebras and study the restrictions of various representations to this subalgebra.
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    Commutative subalgebra of a shuffle algebra associated with quantum toroidal glm|n
    (Elsevier, 2024-06) Feigin, B.; Jimbo, M.; Mukhin, E.; Mathematical Sciences, School of Science
    We define and study the shuffle algebra Shm|n of the quantum toroidal algebra Em|n associated to Lie superalgebra glm|n. We show that Shm|n contains a family of commutative subalgebras Bm|n(s) depending on parameters s=(s1,…,sm+n), ∏isi=1, given by appropriate regularity conditions. We show that Bm|n(s) is a free polynomial algebra and give explicit generators which conjecturally correspond to the traces of the s-weighted R-matrix computed on the degree zero part of Em|n modules of levels ±1.
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    The Maxwell operator with periodic coefficients in a cylinder
    (2018) Filonov, N.; Prokhorov, Andrei; Mathematical Sciences, School of Science
    In the paper we consider the Maxwell operator in a three-dimensional cylinder with coefficients periodic along the axis of a cylinder. It is proved that for cylinders with circular and rectangular cross-section the spectrum of the Maxwell operator is absolutely continuous.