Results 51 to 60 of about 297 (147)

Saturated sets for generalized Cartan matrices

Tsukuba Journal of Mathematics, 1987
Let \(A=(a_{ij})\) be a generalized Cartan matrix, and \((\mathfrak h,\Pi,\Pi^{\vee})\) be a realization of \(A\), where \(\mathfrak h\) is a \(C\)-vector space and \(\Pi^{\vee}=\{h_1,\ldots,h_n\}\), \(\Pi =\{\alpha_1,\ldots,\alpha_n\}\) are linearly independent subsets of \(\mathfrak h\) and the dual space \(\mathfrak h^*\) of \(\mathfrak h ...
Morita, Jun, Wakimoto, Minoru
openaire   +3 more sources

A categorification of combinatorial Auslander–Reiten quivers

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract We provide a categorification of Oh and Suh's combinatorial Auslander–Reiten quivers in the simply laced case. We work within the perfectly valued derived category pvd(ΠQ)$\mathrm{pvd}(\Pi _Q)$ of the 2‐dimensional Ginzburg dg algebra of a Dynkin quiver Q$Q$.
Ricardo Canesin
wiley   +1 more source

Symmetrizability of Integer Interval Cartan Matrices

Journal of Physics: Conference Series, 2019
Abstract In this paper, we extend Cartan matrix to Integer Interval Cartan matrix by using interval arithmetic operation. We compute symmetrizability condition to the Interval Cartan matrix. It also satisfies the condition for this extention of Integer Interval Cartan matrix; here we focus on the theorem along with the illustration.
C. Dineshkumar, K. Gayathri
openaire   +1 more source

Tessellation Groups, Harmonic Analysis on Non‐Compact Symmetric Spaces and the Heat Kernel in View of Cartan Convolutional Neural networks

Fortschritte der Physik, Volume 74, Issue 4, April 2026.
ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré, Federico Milanesio, Marcelo Oyarzo, Matteo Santoro, Mario Trigiante   +4 more
wiley   +1 more source

Quantum Inspired Universal Analog Computation Based on Circuits

Advanced Quantum Technologies, Volume 9, Issue 4, April 2026.
We propose an analog scheme of classical circuit for universal quantum computation. The information is encoded using correlated electrical signals, and the number of the basic computing components employed in our circuit design is consistent with the number of the quantum gate in the quantum circuit.
Hanxu Zhang, Yifan Sun, Xiangdong Zhang
wiley   +1 more source

Chern-Simons theory, Ehrhart polynomials, and representation theory

Journal of High Energy Physics
The Hilbert space of level q Chern-Simons theory of gauge group G of the ADE type quantized on T 2 can be represented by points that lie on the weight lattice of the Lie algebra g up to some discrete identifications.
Chao Ju
doaj   +1 more source

On Totally Geodesic Submanifolds

Axioms
We give a proof of Cartan’s Theorem on totally geodesic submanifolds for real analytic manifolds endowed with a real analytic, torsion-free, affine connection. We apply the theorem to real analytic Hadamard manifolds and, more generally, to real analytic
Antonella Nannicini, Donato Pertici
doaj   +1 more source

Certifying Anosov representations

Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.
Abstract By providing new finite criteria which certify that a finitely generated subgroup of SL(d,R)$\operatorname{SL}(d,\operatorname{\mathbb {R}})$ or SL(d,C)$\operatorname{SL}(d,\mathbb {C})$ is projective Anosov, we obtain a practical algorithm to verify the Anosov condition.
J. Maxwell Riestenberg
wiley   +1 more source

Sublinear bilipschitz equivalence and the quasiisometric classification of solvable Lie groups

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner, and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry certain families of solvable groups which share the same dimension, cone‐dimension and Dehn function ...
Ido Grayevsky, Gabriel Pallier
wiley   +1 more source

Generalisations of Capparelli's and Primc's identities, II: Perfect An−1(1)$A_{n-1}^{(1)}$ crystals and explicit character formulae

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract In the first paper of this series, we gave infinite families of coloured partition identities which generalise Primc's and Capparelli's classical identities. In this second paper, we study the representation theoretic consequences of our combinatorial results.
Jehanne Dousse, Isaac Konan
wiley   +1 more source