A Quantum Version of the Désarménien Matrix
نویسنده
چکیده
We use elements in the quantum hyperalgebra to define a quantum version of the Désarménien matrix. We prove that our matrix is upper triangular with ones on the diagonal and that, as in the classical case, it gives a quantum straightening algorithm for quantum bideterminants. We use our matrix to give a new proof of the standard basis theorem for the q-Weyl module. As well, we show that the standard basis for the q-Weyl module and the basis dual to the standard basis for the q-Schur module are related by the quantum Désarménien matrix.
منابع مشابه
Quantum modeling of light absorption in graphene based photo-transistors
Graphene based optical devices are highly recommended and interested for integrated optical circuits. As a main component of an optical link, a photodetector based on graphene nano-ribbons is proposed and studied. A quantum transport model is presented for simulation of a graphene nano-ribbon (GNR) -based photo-transistor based on non-equilibrium Green’s function method. In the proposed model a...
متن کاملQUANTUM VERSION OF TEACHING-LEARNING-BASED OPTIMIZATION ALGORITHM FOR OPTIMAL DESIGN OF CYCLIC SYMMETRIC STRUCTURES SUBJECT TO FREQUENCY CONSTRAINTS
As a novel strategy, Quantum-behaved particles use uncertainty law and a distinct formulation obtained from solving the time-independent Schrodinger differential equation in the delta-potential-well function to update the solution candidates’ positions. In this case, the local attractors as potential solutions between the best solution and the others are introduced to explore the solution space...
متن کاملGENERALIZED JOINT HIGHER-RANK NUMERICAL RANGE
The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...
متن کاملاثر درهمتنیدگی و چهارچوب نالخت در بازی کوانتومی چهارکیوبیتی
The effect of increasing quantum bits and Unruh effect on quantum Prisoners’ dilemma has been investigated for both entangled and unentangled initial states. The Nash equilibrium, as an important result of quantum game theory, was obtained through the different payoffs resulted from choosing various strategies. It has been shown that the non-inertial frame disturbs the symmetry of the game. Act...
متن کاملBQIABC: A new Quantum-Inspired Artificial Bee Colony Algorithm for Binary Optimization Problems
Artificial bee colony (ABC) algorithm is a swarm intelligence optimization algorithm inspired by the intelligent behavior of honey bees when searching for food sources. The various versions of the ABC algorithm have been widely used to solve continuous and discrete optimization problems in different fields. In this paper a new binary version of the ABC algorithm inspired by quantum computing, c...
متن کامل