The two-parameter deformation of the supergroup GL(1|1), its differential calculus and its Lie algebra

1992 ◽  
Vol 26 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Č. Burdík ◽  
R. Tomášek
Keyword(s):  
Lie Algebra ◽  
Differential Calculus ◽  
Two Parameter ◽  
Parameter Deformation

scholarly journals COMMENT ON THE DIFFERENTIAL CALCULUS ON THE QUANTUM EXTERIOR PLANE

1998 ◽  
Vol 13 (20) ◽  
pp. 1645-1651 ◽  
Author(s):  
SALIH ÇELIK ◽  
SULTAN A. ÇELIK ◽  
METIN ARIK
Keyword(s):  
Symmetry Group ◽  
Differential Calculus ◽  
Baxter Equation ◽  
Oscillator Algebra ◽  
Quantum Deformation ◽  
R Matrix ◽  
Two Parameter ◽  
Parameter Deformation

We give a two-parameter quantum deformation of the exterior plane and its differential calculus without the use of any R-matrix and relate it to the differential calculus with the R-matrix. We prove that there are two types of solutions of the Yang–Baxter equation whose symmetry group is GL p,q(2). We also give a two-parameter deformation of the fermionic oscillator algebra.

scholarly journals TWO-PARAMETER DIFFERENTIAL CALCULUS ON THE h-EXTERIOR PLANE

1998 ◽  
Vol 13 (05) ◽  
pp. 413-418
Author(s):  
SULTAN A. ÇELIK ◽  
SALIH ÇELIK
Keyword(s):  
Phase Space ◽  
Differential Calculus ◽  
Two Dimensional ◽  
Two Parameter

We construct a two-parameter covariant differential calculus on the quantum h-exterior plane. We also give a deformation of the two-dimensional fermionic phase space.

scholarly journals String theory at order α′2 and the generalized Bergshoeff-de Roo identification

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Stanislav Hronek ◽  
Linus Wulff
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Strong Evidence ◽  
Degrees Of Freedom ◽  
Heterotic String ◽  
Lorentz Transformations ◽  
Covariant Formalism ◽  
Double Field Theory ◽  
Two Parameter ◽  
Parameter Deformation

Abstract It has been shown by Marques and Nunez that the first α′-correction to the bosonic and heterotic string can be captured in the O(D, D) covariant formalism of Double Field Theory via a certain two-parameter deformation of the double Lorentz transformations. This deformation in turn leads to an infinite tower of α′-corrections and it has been suggested that they can be captured by a generalization of the Bergshoeff-de Roo identification between Lorentz and gauge degrees of freedom in an extended DFT formalism. Here we provide strong evidence that this indeed gives the correct α′2-corrections to the bosonic and heterotic string by showing that it leads to a cubic Riemann term for the former but not for the latter, in agreement with the known structure of these corrections including the coefficient of Riemann cubed.

scholarly journals Two-Parameter Deformation of the Poincaré Algebra

1997 ◽  
Vol 12 (05) ◽  
pp. 891-901 ◽  
Author(s):  
A. Stern ◽  
I. Yakushin
Keyword(s):  
Quadratic Algebra ◽  
Commuting Operators ◽  
Poincaré Algebra ◽  
Two Parameter ◽  
Parameter Deformation

We examine a two-parameter (ℏ,λ) deformation of the Poincaré algebra which is covariant under the action of SL q(2,C). When λ → 0 it yields the Poincaré algebra, while in the ℏ → 0 limit we recover the classical quadratic algebra discussed previously in Refs. 1 and 2. The analogues of the Pauli–Lubanski vector w and Casimirs p2 and w2 are found and a set of mutually commuting operators is constructed.

scholarly journals The Two-Parameter Higher-Order Differential Calculus and Curvature on a Quantum Plane

2007 ◽  
Vol 17 (4) ◽  
pp. 651-662 ◽  
Author(s):  
M. El Baz ◽  
A. El Hassouni ◽  
Y. Hassouni ◽  
E. H. Zakkari
Keyword(s):  
Differential Calculus ◽  
Higher Order ◽  
Quantum Plane ◽  
Two Parameter

scholarly journals Interval positroid varieties and a deformation of the ring of symmetric functions

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Allen Knutson ◽  
Mathias Lederer
Keyword(s):  
Symmetric Functions ◽  
Schur Functions ◽  
Dimensional Subspace ◽  
Schubert Varieties ◽  
International Audience ◽  
Structure Constants ◽  
Schubert Classes ◽  
K Theory ◽  
Two Parameter ◽  
Parameter Deformation

International audience Define the <b>interval rank</b> $r_[i,j] : Gr_k(\mathbb C^n) →\mathbb{N}$ of a k-plane V as the dimension of the orthogonal projection $π _[i,j](V)$ of V to the $(j-i+1)$-dimensional subspace that uses the coordinates $i,i+1,\ldots,j$. By measuring all these ranks, we define the <b>interval rank stratification</b> of the Grassmannian $Gr_k(\mathbb C^n)$. It is finer than the Schubert and Richardson stratifications, and coarser than the positroid stratification studied by Lusztig, Postnikov, and others, so we call the closures of these strata <b>interval positroid varieties</b>. We connect Vakil's "geometric Littlewood-Richardson rule", in which he computed the homology classes of Richardson varieties (Schubert varieties intersected with opposite Schubert varieties), to Erd&odblac;s-Ko-Rado shifting, and show that all of Vakil's varieties are interval positroid varieties. We build on his work in three ways: (1) we extend it to arbitrary interval positroid varieties, (2) we use it to compute in equivariant K-theory, not just homology, and (3) we simplify Vakil's (2+1)-dimensional "checker games" to 2-dimensional diagrams we call "IP pipe dreams". The ring Symm of symmetric functions and its basis of Schur functions is well-known to be very closely related to the ring $\bigoplus_a,b H_*(Gr_a(\mathbb{C}^{(a+b)})$ and its basis of Schubert classes. We extend the latter ring to equivariant K-theory (with respect to a circle action on each $\mathbb{C}^{(a+b)}$, and compute the structure constants of this two-parameter deformation of Symm using the interval positroid technology above.

scholarly journals On a (p,k)-analogue of the Gamma function and some associated Inequalities

2016 ◽  
Vol 2 (2) ◽  
pp. 79-90 ◽  
Author(s):  
K. Nantomah ◽  
E. Prempeh ◽  
S. B. Twum
Keyword(s):  
Gamma Function ◽  
Two Parameter ◽  
Parameter Deformation

Abstract In this paper, we introduce a new two-parameter deformation of the classical Gamma function, which we call a (p,k)-analogue of the Gamma function. We also provide some identities generalizing those satisfied by the classical Gamma function. Furthermore, we establish some inequalities involving this new function.

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