# On representation theory of quantum $S{L}_{q}\left(2\right)$ groups at roots of unity

Piotr Kondratowicz; Piotr Podleś

Banach Center Publications (1997)

- Volume: 40, Issue: 1, page 223-248
- ISSN: 0137-6934

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topKondratowicz, Piotr, and Podleś, Piotr. "On representation theory of quantum $SL_{q}(2)$ groups at roots of unity." Banach Center Publications 40.1 (1997): 223-248. <http://eudml.org/doc/252182>.

@article{Kondratowicz1997,

abstract = {Irreducible representations of quantum groups $SL_q(2)$ (in Woronowicz’ approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the case of q being an odd root of unity. Here we find the irreducible representations for all roots of unity (also of an even degree), as well as describe “the diagonal part” of the tensor product of any two irreducible representations. An example of a not completely reducible representation is given. Non-existence of Haar functional is proved. The corresponding representations of universal enveloping algebras of Jimbo and Lusztig are provided. We also recall the case of general q. Our computations are done in explicit way.},

author = {Kondratowicz, Piotr, Podleś, Piotr},

journal = {Banach Center Publications},

keywords = {quantum group; quantum enveloping algebra; irreducible representation; Hopf algebra; Haar functional},

language = {eng},

number = {1},

pages = {223-248},

title = {On representation theory of quantum $SL_\{q\}(2)$ groups at roots of unity},

url = {http://eudml.org/doc/252182},

volume = {40},

year = {1997},

}

TY - JOUR

AU - Kondratowicz, Piotr

AU - Podleś, Piotr

TI - On representation theory of quantum $SL_{q}(2)$ groups at roots of unity

JO - Banach Center Publications

PY - 1997

VL - 40

IS - 1

SP - 223

EP - 248

AB - Irreducible representations of quantum groups $SL_q(2)$ (in Woronowicz’ approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the case of q being an odd root of unity. Here we find the irreducible representations for all roots of unity (also of an even degree), as well as describe “the diagonal part” of the tensor product of any two irreducible representations. An example of a not completely reducible representation is given. Non-existence of Haar functional is proved. The corresponding representations of universal enveloping algebras of Jimbo and Lusztig are provided. We also recall the case of general q. Our computations are done in explicit way.

LA - eng

KW - quantum group; quantum enveloping algebra; irreducible representation; Hopf algebra; Haar functional

UR - http://eudml.org/doc/252182

ER -

## References

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