q-Immanants and Higher Quantum Capelli Identities

Abstract: Imminents are generalizations of determinants and permanents. In this talk I will explain how to construct the family of polynomials $S_{\mu}(z)$ indexed by standard Young tableaux whose coefficients are central elements in the quantized algebra $U_q(gl(n))$. For another special value of $z$, they coincide with Okounkov's quantum immanant for the enveloping algebra gl(n). We show that the Harish-Chandra image of $S_{\mu}(z)$ are the factorial Schur functions. We also obtain the quantum analogues of the higher Capelli identities and Newton-type identities for the quantum enveloping algebra. This is joint work with Ming Liu and Alexander Molev.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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