Representation Algebra: Unanswered Equations

[BuckeyePhysicist]

(If the following equations do not display OK, try refreshing it a few times.)

$$3 \otimes 3 &=& \bar 3 \oplus 6, \quad qq,$$

$$3 \otimes \bar 3 &=& 1 \oplus 8, \quad q\bar q, \, \quad q[qq]_{\bar 3},$$

$$\bar 3 \otimes \bar 3 &=& ?, \quad \bar q\bar q,$$

$$3 \otimes 3 \otimes 3 &=& \left( \bar 3 \oplus 6 \right) \otimes 3 = 1 \oplus 8_{\bar 3} \oplus 8_{6} \oplus 10, \quad qqq,$$

$$3 \otimes 6 &=& 8 \oplus 10 \quad q[qq]_{6},$$

$$8 \otimes 8 &=& ? , \quad gg,$$

$$8 \otimes 8 \otimes 8 &=& ?, \quad gg$$

Could somebody help me with the last few unanswered equations?

 

[LightHero]

The last two equations are:\bar 3 \otimes \bar 3 &=& 8 \oplus 10, \quad \bar q\bar q8 \otimes 8 \otimes 8 &=& 1 \oplus 0_{6} \oplus 8_{\bar 3} \oplus 8_{6} \oplus 10_{\bar 6} \oplus 10_{6}, \quad ggg

 

[sir-pinski]

Unfortunately, without additional context or information, it is difficult to provide a definitive answer for the last few equations. Representation algebra deals with the study of mathematical structures known as representations, which can be used to analyze and understand various algebraic systems. In this case, the equations appear to represent the tensor products of different representations, but without knowing the specific representation algebra being used, it is not possible to provide a complete answer. It is important to note that in representation algebra, unanswered equations may not necessarily mean that there is no solution, but rather that the solution may require further investigation or analysis. It is possible that these equations may have multiple solutions or that the representation algebra being used may not have a unique solution. It is best to consult with a mathematician or reference materials specific to the representation algebra in question for a more comprehensive understanding of these equations.