We show a new method for computing the dimensions of the irreducible constituents of W. Further, we apply this method to Majorana representations of the symmetric groups and prove that the symmetric group has a Majorana representation in which every permutation of type (2, 2) of corresponds to...
These tools are then applied to the representation theory of symmetric groups. In particular, we present an algorithm which efficiently computes for every skew module of a symmetric group an R-basis which is adapted to a Specht series. This result is a constructive, characteristic-free analogue ...
We implement a finite-dimensional representation of the 2+1D Lorentz group with a PT-symmetric waveguide array. Our device can be engineered to behave like... BM Rodríguez-Lara,J Guerrero - 《Optics Letters》 被引量: 8发表: 2015年 The Geometry of Optimal Control Solutions on some Six Dimen...
Humphreys, J.: Introduction to Lie Algebras and Representation Theory. Springer-Verlag, New York (1972) MATH Google Scholar Iliev, P., Terwilliger, P.: The Rahman polynomials and the Lie algebra \mathfrak{sl} _3(\mathbb{C} ). Transactions of the American Mathematical Society. 364, 4225–...
Harmonic decomposition: the case of Gln. Preprint Kim, S.: Standard monomial theory for flag algebras of GL(n) and Sp(2n). J. Algebra 320(2), 534–568 (2008) Article MathSciNet Google Scholar Kim, S.: The nullcone in the multi-vector representation of the symplectic group and ...
For convenience, the natural logarithmic function in this equation is transformed to the logarithmic function of base 10, which yields [7.24]E−E0−2.303RTnFlogCcDdAaBb Equation [7.24] can be applied to determine the electrode potential at non-standard conditions. This representation of Nernst’...
The sl 3 spider is a diagrammatic category used to study the representation theory of the quantum group U q (sl 3). The morphisms in this category are generated by a basis of non-elliptic webs. Khovanov–Kuperberg observe that non-elliptic webs are indexed by semistandard Young tableaux...
Each column of the 4x4 matrix representation of the State is multiplied by polynomial a(x) = {03}x3 + {01}x2 + {01}x + {02} and reduced modulo x4 + 1. Here, { } denotes an element in AES-GF256-Field. The equations that define MixColumns are detailed ...
We give an elementary and easily computable basis for the Demazure modules in the basic representation of the affine Lie algebra sl^n (and the loop group SL^n). A novel feature is that we define our basis “bottom-up” by raising each extremal weight vector, rather than “top-down” by...
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