On the K–theory of coordinate axes in affine
space

AbstractThe present essay investigates the potential of generative representation applied to the study of relief perspective architectures realized in Italy between the sixteenth and seventeenth centuries. In arts, and architecture in particular, relief perspective is a three-dimensional structure able to create the illusion of great depths in small spaces. A method of investigation applied to the case study of the Avila Chapel in Santa Maria in Trastevere in Rome (Antonio Gherardi 1678) is proposed. The research methodology can be extended to other cases and is based on the use of a Relief Perspective Camera, which can create both a linear perspective and a relief perspective. Experimenting mechanically and automatically the perspective transformations from the affine space to the illusory space and vice versa has allowed us to see the case study in a different light.

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Wilson loop algebras and quantum K-theory for Grassmannians

Journal of High Energy Physics ◽

10.1007/jhep10(2020)036 ◽

2020 ◽

Vol 2020 (10) ◽

Author(s):

Hans Jockers ◽

Peter Mayr ◽

Urmi Ninad ◽

Alexander Tabler

Keyword(s):

Wilson Loop ◽

Gauge Theories ◽

Wilson Line ◽

Quantum Cohomology ◽

Three Dimensional ◽

Loop Algebra ◽

Loop Algebras ◽

Verlinde Algebra ◽

K Theory ◽

Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

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A multiplicative K-theoretic model of Voevodsky’s motivic K-theory spectrum

Journal of Homotopy and Related Structures ◽

10.1007/s40062-018-0227-1 ◽

2018 ◽

Vol 14 (3) ◽

pp. 663-690

Author(s):

Youngsoo Kim

Keyword(s):

Theoretic Model ◽

K Theory

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Toward AGT for Parabolic Sheaves

International Mathematics Research Notices ◽

10.1093/imrn/rnaa308 ◽

2020 ◽

Author(s):

Andrei Neguţ

Keyword(s):

Field Theory ◽

Gauge Theory ◽

Conformal Field Theory ◽

Moduli Spaces ◽

Type A ◽

Conformal Field ◽

Toroidal Algebra ◽

Agt Correspondence ◽

K Theory ◽

The Ideal

Abstract We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.

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