Quantum grothendieck program

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August undefined, 2024

"Esquisse d'un Programme" (Sketch of a Programme) is a famous proposal for long-term mathematical research made by the German-born, French mathematician Alexander Grothendieck in 1984. He pursued the sequence of logically linked ideas in his important project proposal from 1984 until 1988, but his proposed research continues to date to be of major interest in several branches of advanced mathematics. Grothendieck's vision provides inspiration today for several … WebSep 5, 2011 · Download PDF Abstract: We obtain a presentation of the t-deformed Grothendieck ring of a quantum loop algebra of Dynkin type A, D, E. Specializing t at the …

(PDF) Quantum Grothendieck Polynomials - ResearchGate

Web19 GT and Quantum mechanics: EPR and Bell’s inequality 63 20 Trilinear counterexamples 66 21 Some open problems 69 ... an analogue of Grothendieck’s program was developed … Web"Esquisse d'un Programme" (Sketch of a Programme) is a famous proposal for long-term mathematical research made by the German-born, French mathematician Alexander Grothendieck in 1984. He pursued the sequence of logically linked ideas in his important project proposal from 1984 until 1988, but his proposed research continues to date to be … first burmese empire

Quantum Grothendieck rings as quantum cluster algebras

WebJul 27, 2024 · t-deformation called the quantum Grothendieck ring, whic h is contained in some quantum torus Y t . The quantum Grothendieck ring w as ﬁrst studied by Nak ajima [ 42 ] and Varagnolo–V asserot WebOne remarkable point is that they include the isomorphisms between the quantum Grothendieck ring of a simply-laced type and that of a non-simply-laced type. It leads to new positivity results for the simple $(q, t)$-characters in the non-simply-laced cases, and proposes a new cluster algebraic approach for studying the simple $(q, t)$-characters. first burger king commercial

Perverse Sheaves and Quantum Grothedieck Rings SpringerLink

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Web2024-04-16 to present 特定研究員 / Program-Specific Researcher (数理解析研究所 / Research Institute for Mathematical Sciences (RIMS)) Employment Show more detail. Source: Kyoto ... Isomorphisms among quantum Grothendieck rings and propagation of positivity. Journal für die reine und angewandte Mathematik (Crelles Journal) WebSep 5, 2011 · We obtain a presentation of the t-deformed Grothendieck ring of a quantum loop algebra of Dynkin type A, D, E. Specializing t at the the square root of the cardinality of a finite field F, we obtain an isomorphism with the derived Hall algebra of the derived category of a quiver Q of the same Dynkin type. Along the way, we study for each choice of … evaluation of metformin effectivenessWebThe Grothendieck–Teichmüller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this … evaluation of messerschmidt

"WebSep 5, 2011 · We obtain a presentation of the t-deformed Grothendieck ring of a quantum loop algebra of Dynkin type A, D, E. Specializing t at the the square root of the cardinality … " - Quantum grothendieck program

Quantum grothendieck program

[2212.11663] Grothendieck bound in a single quantum system

WebApr 13, 2024 · The EY organization and IBM today announced today that EY Global Services Limited will be joining the IBM Quantum Network, further enabling EY teams to explore solutions with IBM that could help resolve some of today’s most complex business and global challenges. The EY organization will gain access to IBM’s fleet of quantum … WebAug 3, 2010 · Let kG be a group algebra, and D(kG) its quantum double.We first prove that the structure of the Grothendieck ring of D(kG) can be induced from the Grothendieck ring …

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WebSep 9, 2006 · Quantum K-theory is a K-theoretic version of quantum cohomology, which was recently defined by Y.-P. Lee. Based on a presentation for the quantum K-theory of the classical flag variety Fl_n, we ... WebFrenkel, E. and Reshetikhin, N., The q-characters of representations of quantum affine algebras and deformations of W-algebrasContemporary Math.248 (2000), 163–205. CrossRef MathSciNet Google Scholar Ginzburg, V. and Vasserot, E., Langlands reciprocity fo affine quantum groups of typeA n Internat. Math. Res.

WebApr 30, 2024 · We establish ring isomorphisms between quantum Grothendieck rings of certain remarkable monoidal categories C Q, B n and C Q, A 2 n − 1 of finite-dimensional representations of quantum affine algebras of types B n (1) and A 2 n − 1 (1), respectively.Our proof relies in part on the corresponding quantum cluster algebra … WebMar 21, 2024 · The program is named after Robert ... connects to the work of Alexander Grothendieck, ... for the objects that satisfy analogues of the Schrödinger equation” from …

WebFeb 1, 2024 · We define and construct a quantum Grothendieck ring for a certain monoidal subcategory of the category $\\mathcal{O}$ of representations of the quantum loop … WebAug 9, 2006 · Quantum K-theory is a K-theoretic version of quantum cohomology, which was recently defined by Y.-P. Lee. Based on a presentation for the quantum K-theory of the …

WebApr 6, 2024 · We establish a cluster theoretical interpretation of the isomorphisms of [F.-H.-O.-O., J. Reine Angew. Math., 2024] among quantum Grothendieck rings of representations of quantum loop algebras. Consequently, we obtain a quantization of the monoidal categorification theorem of [Kashiwara-Kim-Oh-Park, arXiv:2103.10067]. We establish …

WebFrenkel–Reshetikhin's conjecture stated that for more general quantum integrable systems, constructed via finite-dimensional representations of the quantum affine algebra U q (g ̂) … first burn hamilton meaningWebFeb 28, 2024 · We first compute the denominator formulas for quantum affine algebras of all exceptional types. Then we prove the isomorphisms among Grothendieck rings of categories ${C_Q^{(t)} (t=1,2,3), \mathscr{C}_{\mathscr{Q}}^{(1)}}$ and ${\mathscr{C}_{\mathfrak{Q}}^{(1)}}$.These results give Dorey’s rule for all exceptional … evaluation of metoprolol effectivenessWebMar 18, 2024 · quantum Grothendieck ring K t (C), which is a t-deformation of K (C) in a certain quantum. torus [54, 60]. ... F ramework Programme H2024 with ERC Grant Agreement number 647353 Qaﬃne. evaluation of marketisation sociologyWebNov 7, 2024 · Grothendieck’s bound is used in the context of a single quantum system, in contrast to previous work which used it for multipartite entangled systems and the … first burleson bank burleson texasWebNov 29, 2024 · We establish a quantum cluster algebra structure on the quantum Grothendieck ring of a certain monoidal subcategory of the category of finite-dimensional representations of a simply-laced quantum affine algebra. Moreover, the (q,t)-characters of certain irreducible representations, among which fundamental representations, are … evaluation of marketing business planWebWe establish a quantum cluster algebra structure on the quantum Grothendieck ring of a certain monoidal subcategory of the category of finite-dimensional representations of a simply-laced quantum affine algebra. Moreover, the (q, t)-characters of certain irreducible representations, among which fundamental representations, are obtained as quantum … first burn hamilton music videoWebDec 22, 2024 · Grothendieck's bound is used in the context of a single quantum system, in contrast to previous work which used it for multipartite entangled systems and the … first burn hamilton animatic