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http://hdl.handle.net/2433/24849
2022-10-02T05:56:09ZLow regularity a priori estimate for KDNLS via the short-time Fourier restriction method
http://hdl.handle.net/2433/276397
Title: Low regularity a priori estimate for KDNLS via the short-time Fourier restriction method
Authors: KISHIMOTO, Nobu; TSUTSUMI, Yoshio
Abstract: In this article, we consider the kinetic derivative nonlinear Schrödinger equation (KDNLS), which is a one-dimensional nonlinear Schrödinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. For the Cauchy problem both on the real line and on the circle, we apply the short-time Fourier restriction method to establish a priori estimate for small and smooth solutions in Sobolev spaces H[s] with s > 1/4.
Description: Dedicated to the memory of Professor Jean Ginibre2022-09-01T00:00:00ZContinuous Functions on Final Comodels of Free Algebraic Theories
http://hdl.handle.net/2433/276396
Title: Continuous Functions on Final Comodels of Free Algebraic Theories
Authors: YOSHIDA, Tomoya
Abstract: In 2009, Ghani, Hancock and Pattinson gave a tree-like representation of stream processors A[N] → B[N]. In 2021, Garner showed that this representation can be established in terms of algebraic theory and comodels: the set of infinite streams A[N] is the final comodel of the algebraic theory of A-valued input [T][A] and the set of stream processors Top(A[N] , B[N]) can be seen as the final [T][A]-[T][B]-bimodel. In this paper, we generalize Garner's results to the case of free algebraic theories.2022-09-01T00:00:00ZQuantum Langlands duality of representations of 𝓦-algebras
http://hdl.handle.net/2433/276289
Title: Quantum Langlands duality of representations of 𝓦-algebras
Authors: Arakawa, Tomoyuki; Frenkel, Edward
Abstract: We prove duality isomorphisms of certain representations of W-algebras which play an essential role in the quantum geometric Langlands program and some related results.2019-12-01T00:00:00ZW-algebras as coset vertex algebras
http://hdl.handle.net/2433/276288
Title: W-algebras as coset vertex algebras
Authors: Arakawa, Tomoyuki; Creutzig, Thomas; Linshaw, Andrew R.
Abstract: We prove the long-standing conjecture on the coset construction of the minimal series principal W-algebras of ADE types in full generality. We do this by first establishing Feigin’s conjecture on the coset realization of the universal principal W-algebras, which are not necessarily simple. As consequences, the unitarity of the “discrete series” of principal W-algebras is established, a second coset realization of rational and unitary W-algebras of type A and D are given and the rationality of Kazama–Suzuki coset vertex superalgebras is derived.2019-10-01T00:00:00Z