Many in the audience were intrigued when, at the end of the ceremony, Mulayam Singh Yadav walked up to Prime Minister Narendra Modi and whispered something in his ear.
A senior BJP politician who was standing close to them told The Telegraph that he had been able to overhear snatches of the conversation.
" Thoda Akhilesh ka khayal rakhiye (Please take care of Akhilesh)" was what the Samajwadi Party patriarch told the Prime Minister, according to the BJP source who wishes to remain anonymous.
Akhilesh, Mulayam's son and the chief minister Adityanath had replaced, was standing at a corner of the dais. Mulayam could be seen motioning to his son, who immediately walked up to the Prime Minister.
While the son shook hands with Modi, the father placed both his hands over their locked palms for a few seconds and apparently said: " Inko sikhaiye (Teach him please)."
"I reckon Mulayam was asking Modi to teach Akhilesh the intricacies of politics," the BJP source said. "Modi didn't disappoint Mulayam. He patted Akhilesh on the right shoulder."
Mulayam's purported gesture appears at odds with the public perception that he is furious with his son, who had seized the party's reins from him in a coup in January, prompting him to largely stay away from the election campaign.
Mulayam Singh Yadav greeting PM Modi at Yogi Adityanath's swearing-in ceremony in Lucknow on Sunday. PIC/ABP News.
But some have insisted that Mulayam's apparent anger was meant just for public consumption - to save his own face and keep peace within his family, since his brother Shivpal and second wife Sadhana Gupta are bitterly opposed to Akhilesh.
During the Assembly election campaign, Modi had targeted Akhilesh for making a "new friend" - a jab at his alliance with Congress vice-president Rahul Gandhi.
Akhilesh had retaliated by ridiculing how "Gujarat's donkeys" were being advertised - an ostensible reference to a wildlife video that drew laughs at a poll rally with its all-too-apparent implication.
But, while the Bahujan Samaj Party and the Congress spurned invites to the swearing-in, Mulayam and Akhilesh turned up as the only non-NDA guests.
Mulayam, who has a disproportionate assets case pending against him and his family members in the Supreme Court, has always had good personal relations with the BJP brass.
Senior Samajwadi politicians whom this newspaper contacted declined any comment on "whisper politics".
When a simmering feud between Shivpal and Akhilesh had exploded in public last September, with Sadhana allegedly fanning the flames, Mulayam had appeared to side with his brother. He even temporarily suspended Akhilesh from the party in late December.
Akhilesh then dethroned Mulayam as Samajwadi national president at a disputed party convention on January 1. He then won the party symbol for his faction from the Election Commission, beating back a challenge from Mulayam.
During the campaign, Mulayam addressed just two rallies, one for Shivpal and the other for Sadhana's daughter-in-law Aparna Yadav.
-The Telegraph, Calcutta