In what ways is the author reflected in the novel?

THe guy spent many years in a Soviet labour camp so I'd say he pretty much knows what he is talking about. Check out this quote from Wikepedia,

In February 1945, while serving in East Prussia, Solzhenitsyn was arrested for writing derogatory comments in letters to a friend, Nikolai Vitkevich... He was accused of anti-Soviet propaganda under Article 58 paragraph 10 of the Soviet criminal code, and of "founding a hostile organization" under paragraph 11.[15] Solzhenitsyn was taken to the Lubyanka prison in Moscow, where he was beaten and interrogated. On 7 July 1945, he was sentenced in his absence by Special Council of the NKVD to an eight-year term in a labor camp.

I have no doubt that these experieces are what he drew inspiration from to write his novel.