# Lie Elements and Knuth Relations

@article{Schocker2002LieEA, title={Lie Elements and Knuth Relations}, author={Manfred Schocker}, journal={Canadian Journal of Mathematics}, year={2002}, volume={56}, pages={871 - 882} }

Abstract A coplactic class in the symmetric group ${{\mathcal{S}}_{n}}$ consists of all permutations in ${{\mathcal{S}}_{n}}$ with a given Schensted $Q$ -symbol, and may be described in terms of local relations introduced by Knuth. Any Lie element in the group algebra of ${{\mathcal{S}}_{n}}$ which is constant on coplactic classes is already constant on descent classes. As a consequence, the intersection of the Lie convolution algebra introduced by Patras and Reutenauer and the coplactic…

## 16 Citations

### On the Garsia Lie Idempotent

- MathematicsCanadian Mathematical Bulletin
- 2005

Abstract The orthogonal projection of the free associative algebra onto the free Lie algebra is afforded by an idempotent in the rational group algebra of the symmetric group ${{S}_{n}}$ , in each…

### Color-dressed string disk amplitudes and the descent algebra

- Mathematics
- 2021

Inspired by the definition of color-dressed amplitudes in string theory, we define analogous color-dressed permutations replacing the color-ordered string amplitudes by their corresponding…

### The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2021

We study the Kawai–Lewellen–Tye (KLT) relations for quantum field theory by reformulating it as an isomorphism between two Lie algebras. We also show how explicit formulas for KLT relations arise…

### Non-abelian Z-theory: Berends-Giele recursion for the α′-expansion of disk integrals

- Geology
- 2016

A bstractWe present a recursive method to calculate the α′-expansion of disk integrals arising in tree-level scattering of open strings which resembles the approach of Berends and Giele to gluon…

### Non-abelian Z-theory: Berends-Giele recursion for the α′-expansion of disk integrals

- MathematicsJournal of High Energy Physics
- 2017

We present a recursive method to calculate the α′-expansion of disk integrals arising in tree-level scattering of open strings which resembles the approach of Berends and Giele to gluon amplitudes.…

### KK-like relations of α′ corrections to disk amplitudes

- MathematicsJournal of High Energy Physics
- 2022

Inspired by the definition of color-dressed amplitudes in string theory, we define analogous color-dressed permutations replacing the color-ordered string amplitudes by their corresponding…

### All-order differential equations for one-loop closed-string integrals and modular graph forms

- MathematicsJournal of High Energy Physics
- 2020

We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories. These closed-string integrals…

### Two dialects for KZB equations: generating one-loop open-string integrals

- MathematicsJournal of High Energy Physics
- 2020

Two different constructions generating the low-energy expansion of genus-one configuration-space integrals appearing in one-loop open-string amplitudes have been put forward in refs. [1–3]. We are…

### Berends-Giele recursion for double-color-ordered amplitudes

- Physics
- 2016

A bstractTree-level double-color-ordered amplitudes are computed using Berends-Giele recursion relations applied to the bi-adjoint cubic scalar theory. The standard notion of Berends-Giele currents…

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