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Some authors talk about Gamma Sagittarii as a single star, while others use Gamma1 Sgr for W Sgr and Gamma2 Sgr for 10 Sgr (Gamma Sgr being then ambiguous). SIMBAD database uses Gamma1/Gamma2 as of 2017, for example, while Richard Hinckley Allen only talks about Gamma (1899).

Note that the original Bayer designation did not include superscript, and was referred only to what is today known as Gamma2 Sgr.

Some authors did introduce superscripts to some double stars; some stayed (as for example Beta1 Sgr and Beta2 Sgr), while others did not (such as Gamma2 UMi, or Pherkad, and Gamma1 UMi, mostly known as 11 UMi; SIMBAD displays only Gamma UMi for Pherkad).

When did the change for the case of Gamma Sgr happen? Was there a specific event when this was standardised? (Such as when Eugène Delporte published the Atlas Céleste in 1930, accepted by the IAU to delimit the constellations, and hence getting rid of the Delta Pegasi designation in favour of Alpha Andromedae).

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I will self-answer my question: it seems the event I was wondering about (in which Gamma Sgr became officially Gamma2 Sgr) was the 20th IAU General Assembly in 1988, Baltimore (Maryland, United States). It was decided there that Bayer and Flamsteed designations accepted would be those found in the 4th edition of the The Bright Star Catalogue (1982). By the way, this catalogue is the same introducing the HR (for "Harvard Revised") codes for stars. Thanks to Eric Mamajek for his email clarification on this.

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