Abstract

The continuum hypothesis has been unsolved for hundreds of years. In other words, can I answer it completely? By refuting the culturally responsible continuum [1], one can link the problem to the mathematical continuum, and it is possible to disproof the continuum hypothesis [2] . To go ahead a step, one may extend our mathematical system (by employing a more powerful set theory) and solve the continuum problem by three conditional cases. This event is sim-ilar to the status cases in the discriminant of solving a quadratic equation. Hence, my proposed al-gorithmic flowchart can best settle and depict the problem. From the above, one can further con-clude that when people extend mathematics (like set theory — ZFC) into new systems (such as Force Axioms), experts can solve important mathematical problems (CH). Indeed, there are differ-ent types of such mathematical systems, similar to ancient mathematical notation. Hence, different cultures have different ways of representation, which is similar to a Chinese saying: “different vil-lages have different laws.” However, the primary purpose of mathematical notation was initially to remember and communicate. This event indicates that the basic purpose of developing any new mathematical system is to help solve a natural phenomenon in our universe.

Highlights

  • Let be a Lie algebra of all matrices of order

  • We work with finite-dimensional modules and finite-dimensional representation of

  • Choose integers, such that the inequality is satisfied. These partitions are quite important because they appear to be the core in constructing representations. These chosen integers are used to construct some index set

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Summary

Introduction

Let be a Lie algebra of all matrices of order. In this paper, we work with finite-dimensional modules and finite-dimensional representation of. Choose integers , , , such that the inequality is satisfied These partitions are quite important because they appear to be the core in constructing representations. L. Tsetlin gave an explicit construction of a basis for every simple finitedimensional module of. Tsetlin gave an explicit construction of a basis for every simple finitedimensional module of In their work, they gave all the irreducible representations of general linear algebra ( ). E. Ramirez provided a classification and explicit bases of tableaux of all irreducible generic Gelfand-Tsetlin modules for the Lie algebra [2]. This paper will show that the Gelfand-Tsetlin constructions given in the year [1] forms all the irreducible representations of special linear algebra by providing proofs to results.

Notations and Preliminaries
Main Results
Conclusion

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