Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Plethystic algebras and vector symmetric functions.

G C Rota1, J A Stein

  • 1Massachusetts Institute of Technology, Cambridge, MA 02139, USA.

Proceedings of the National Academy of Sciences of the United States of America
|December 20, 1994
PubMed
Summary

We establish an isomorphism between the plethystic Hopf algebra Pleth(Super[L]) and vector symmetric functions. The Hall inner product is extended to this Hopf algebra, advancing symmetric function theory.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Highlighting the need for prospective randomized studies on the management of dysplastic naevi.

The British journal of dermatology·2018
Same author

The role of access to care in acral lentiginous melanoma survival.

The British journal of dermatology·2017
Same author

Meta-analysis concerning mortality for pregnancy-associated melanoma.

Journal of the European Academy of Dermatology and Venereology : JEADV·2015
Same author

Bullous systemic contact dermatitis caused by an intra-articular steroid injection.

The British journal of dermatology·2014
Same author

Brood parasitism and the evolution of cooperative breeding in birds.

Science (New York, N.Y.)·2013
Same author

Thyroid Function in the Euthyroid Parents of Three Non-endemic Goitrous Cretins.

British medical journal·2010

Area of Science:

  • Algebraic Combinatorics
  • Representation Theory
  • Hopf Algebras

Background:

  • The study of symmetric functions is crucial in combinatorics and representation theory.
  • Hopf algebras provide a powerful framework for algebraic structures.
  • Plethystic algebra offers advanced tools for symmetric functions.

Purpose of the Study:

  • To establish a structural link between plethystic Hopf algebras and vector symmetric functions.
  • To extend the applicability of the Hall inner product within Hopf algebra theory.

Main Methods:

  • Establishing an algebraic isomorphism between Pleth(Super[L]) and the algebra of vector symmetric functions.
  • Generalizing the Hall inner product to the Pleth(Super[L]) Hopf algebra.

Related Experiment Videos

Main Results:

  • A concrete isomorphism is demonstrated between Pleth(Super[L]) and vector symmetric functions.
  • The Hall inner product is successfully extended to the Pleth(Super[L]) Hopf algebra.

Conclusions:

  • This work bridges plethystic Hopf algebras and vector symmetric functions.
  • The extension of the Hall inner product enriches the study of symmetric functions within Hopf algebra contexts.