Related papers: Included-row exchange principle for quantum minors
The purpose of this paper is to explain how the identities of various fundamental lemmas fall within the scope of the transfer principle, a general result that allows to transfer theorems about identities of p-adic integrals from one…
For any homogeneous identity between $q$-minors, we provide an identity between $P,Q$-minors.
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT)…
An exchangeable random matrix is a random matrix with distribution invariant under any permutation of the entries. For such random matrices, we show, as the dimension tends to infinity, that the empirical spectral distribution tends to the…
We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…
Complete sets of commutation relations for arbitrary pairs of quantum minors are computed, with explicit coefficients in closed form.
In this article we develop the theory of minors of non-commutative schemes. This study is motivated by applications in the theory of non-commutative resolutions of singularities of commutative schemes. In particular, we construct a…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
In this paper we compute explicit formulas for the commutation relations among quantum minors in the quantum matrix bialgebra $\cO_q(M_n(k))$.
We give a complete combinatorial characterization of homogeneous quadratic relations of "universal character" valid for minors of quantum matrices (more precisely, for minors in the quantized coordinate ring $O_q(M_{m,n}(K))$ of $m\times n$…
The algebra of quantum matrices of a given size supports a rational torus action by automorphisms. It follows from work of Letzter and the first named author that to understand the prime and primitive spectra of this algebra, the first step…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.
Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers,…
Within context of quantum logic, it is possible to assign dispersion-free probabilities to experimental propositions pertaining to qubits. This makes qubits distinct from the rest of quantum systems since the latter do not admit…
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
We propose the principle, the law of statistical balance for basic physical observables, which specifies quantum statistical theory among all other statistical theories of measurements. It seems that this principle might play in quantum…
We prove First Fundamental Theorems of Coinvariant Theory for the standard coactions of the quantum general and special linear groups on tensor products of quantum matrix algebras. More precisely, let m,n,t be arbitrary positive integers,…