login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A121214 Dimensions of the irreducible representations of the algebraic group SL4 (equivalently, simple Lie algebra of type A3) over the complex numbers, listed in increasing order. 3
1, 4, 6, 10, 15, 20, 35, 36, 45, 50, 56, 60, 64, 70, 84, 105, 120, 126, 140, 160, 165, 175, 189, 196, 216, 220, 224, 256, 270, 280, 286, 300, 315, 336, 360, 364, 384, 396, 420, 440, 455, 480, 500, 504, 540, 560, 594, 616, 630, 640, 680, 715, 729, 735, 750, 756 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

We include "1" for the 1-dimensional trivial representation and we list each dimension once, ignoring the fact that inequivalent representations may have the same dimension.

REFERENCES

N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Springer, 2002.

J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.

LINKS

Table of n, a(n) for n=1..56.

Wikipedia, Special linear group

FORMULA

Given a vector of 3 nonnegative integers, the Weyl dimension formula tells you the dimension of the corresponding irreducible representation. The list of such dimensions is then sorted numerically.

EXAMPLE

The highest weight 000 corresponds to the 1-dimensional module on which SL4 acts trivially. The standard representation and its dual have dimension 4 (the second term in the sequence) and highest weights 100 and 001. The third term in the sequence, 6, is the dimension of the representation of SL4 on the second exterior power of the standard representation; it has highest weight 010. The fourth term, 10, is the dimension of the second symmetric power of the standard representation or its dual, with highest weight 200 or 002. The fifth term, 15, corresponds to the adjoint representation with highest weight 101.

PROG

(GAP) # see program at A121732

CROSSREFS

Cf. A121732, A121741.

Sequence in context: A310585 A179445 A310586 * A219047 A116996 A004399

Adjacent sequences:  A121211 A121212 A121213 * A121215 A121216 A121217

KEYWORD

nonn

AUTHOR

Skip Garibaldi (skip(AT)member.ams.org), Aug 20 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 19:06 EST 2018. Contains 318151 sequences. (Running on oeis4.)